The question cites two links, but neither of them raise as a claim the question of how long it takes for a renewable energy system to recoup its energy cost, which is the title of the question. First I'll address the very broad question in the title, for which no notable claim was cited (but which will exist somewhere out there).
The two links cited raise two other claims, and I'll address those two after that. The first claims that there are times when power consumption by wind turbines for their own management, exceeds their generation. The second claims that total mean power generation by the world's installed PV systems has only recently exceeded the total mean power consumption used by the world's PV manufacturers.
Claim 1: More fossil-powered energy is spent on producing these power-generating devices than these devices themselves would produce
tl;dr: false. Onshore wind produces around 20-80 times as much energy as is required to produce the turbines. Offshore wind about 10-20 times. PV around 10-20 times.
As the question mentions large-scale wind and PV, I'll just focus on that subset of renewables. I'll look at energy payback time, and lifetime, both measured in years. As long as lifetime exceeds energy payback time (EPBT), then more electricity is generated than is consumed in its construction. And if generation exceeds total energy consumed, it must also exceed total fossil-fuel consumption used, as that cannot be greater than total energy consumed.
EPBT(y) life(y) sources
LARGE-SCALE WIND: ,,,,8]
onshore 0.25-1 20-25
offshore 1-2 20-25?
monocrystalline silicon 1.7-2.7 25+
polycrystalline silicon 1.7-2.2 20-25
CdTe 0.8-1.1 10-25
Sources: 1, 2, 3,pdf, 4,pdf, 5, pdf, 6, 7, 8 - a mixture of independent studies, peer-reviewed journal papers, and manufacturers' information, which are all broadly consistent on the range of numbers.
Note 1: We don't know how long monocrystalline PV will last, because it's only been around for a few decades in commercial form. We do know that after 20-30 years, the cells can be stripped of their old encapsulation and re-encapsulated (pdf). Similarly, we can only estimate the lifetime of commercial offshore windfarms as 20-25 years, as the first such farm, at Vindeby, is stil generating now, having been built in 1991 (more numbers in my blogpost on capacity factors at Danish offshore wind farms).
Note 2: different studies make different assumptions about the level of wind/solar resource available at the actual site; about how much energy is used for operations, maintenance and decommissioning (and this are indeed generally included in lifecycle cost analyses, as you'll see from most of those references explicitly); and about the manufacturing specifics. These can result in wide variations in the estimates. Onshore wind only reached maturity around 2002 (which means we haven't yet done a full lifecycle for modern onshore wind turbines yet); the others are still in the phase of disruptive innovation; so there's no meaningful empirical whole-lifecycle data available yet.
Claim 2: there are times when power consumption by wind turbines for their own management, exceeds their generation.
tl;dr: False for recent years; true on occasion before 2003. It's rare, but it has happened: I could find no occurrence of it in the data for Britain, but some instances of it happening in Denmark in 2000 and 2002.
Indeed, it can happen to any type of generation: gas plants, coal plants, nuclear plants, hydro plants, etc: they all use some amount of electricity for background operations, even when they're not generating: lights in the control room, cooling equipment, whatever.
It's more noticeable for wind, because of the nature of common-cause (aka common-mode) lack of generation. All forms of generations are susceptible to common-cause lack of generation, where (almost) no plants of a particular type in a specific country are generating electricity at a given moment. For example, Japan's nuclear fleet had many months of common-cause lack of generation after the 2011 earthquake & tsunami. But electricity was still being consumed at those sites, so the whole nuclear fleet was a net consumer of electricity. Similarly, if a country's supply of coal or natural gas were interrupted, that whole generation fleet would go offline at the same time, but skeleton operations would continue at plants, to ensure they were ready for operation when fuel supplies resumed.
For wind, where the whole generation fleet is within the same climatic area, there can be times when total generation is very low (of the order of 0.5% or so) of total nameplate capacity, and at those times, the operational electricity consumption of the turbines, for de-icing and standby mode, can exceed total wind generation. This has happened in Denmark, over a decade ago, but not since; I couldn't find any occasion in the data of it happening in Britain. The cited link, claims it got its story from a columnist in a downmarket English newspaper: that columnist doesn't cite the source of his data, nor the specific date and time, just that it was a few weeks before 21 December 2010. However, examining the Elexon half-hourly grid data (data free with registration) that covers the period from 1 November 2008 to now, there was no time when net mean half-hourly wind generation was less than zero. The lowest mean half-hourly output was 2MW, for the period 0700-0730 (UTC+1) on 5 June 2010. There are no times times in the instantaneous 5-minute data where it happened, either, over the same period. There is a period of corrupt data in the record, around 19 October 2010, where net output for generation (coal, gas, wind) are all shown as zero (which is impossible, as it would have caused a national blackout, and that didn't happen then), and it may be that that corrupt data is the origin of the story.
However, looking at the Danish data, it had happened in the past in Denmark, that net generation from wind was negative, as turbine own-power consumption was greater than total turbine generation: sixteen half-hourly intervals in 2000; one half-hourly interval in 2002; nothing since then. It's not that surprising that it hasn't happened since: turbine control technology has improved, and a lot of older turbines were phased out in 2002 as part of a national repowering programme.
Claim 3: total mean power generation by the world's installed PV systems has only recently exceeded the total mean power consumption used by the world's PV manufacturers.
tl:dr: probably true as of 2012; impossible to verify, but entirely plausible.
Without a particular reason to be sceptical, I don't see any reason to doubt the conclusions of the peer-reviewed paper cited. The data necessary to make the calculation isn't available, so one is left with partial information and best professional estimates, both of total global PV generation in a year, and of total energy consumption by PV manufacturers in a year. We can make a good estimate of the former, because almost all PV is now grid-connected, and a proportion of it (one that is likely to be decently representative) is metered. It's much harder to make a good estimate of the latter, because there are so many factories involved in the different stages of PV production, all over the world, and they don't have to report their energy consumption. So the paper in question estimates energy consumption, by combining estimates of total manufacturing output, and known figures for some fabricators for unit input energy per unit manufactured capacity.
It's a plausible number, even though PV energy payback times tend to be of the order of 3 years, and that's because although the expansion of installed PV capacity has been so very fast: of the order of 70% per year, averaged over several years. We can do a crude back-of-envelope calculation to see how that works:
Year Generation new capacity total capacity Power consumption
1 0 10 10 30
2 10 17 27 51
3 27 29 56 87
4 56 49 105 147
5 105 83 189 251
It's a simplified calculation, showing capacity in terms of mean generation (rather than nameplate capacity; year 3 generation is same as total capacity at the end of year 2; year 3 power consumption is three times the new capacity built in year 3; to simplify the calculation, I've assumed that it all comes online only at the very end of the year it's manfactured). PV generation will only exceed PV production when that exponential growth starts levelling off (as it will, of course, in time), and/or energy payback times reduce even further.
And this is going to be true of any new generation technology that expands very fast, relative to its energy payback period: for a 4-year energy payback, it will be true for any growth rate over 25% per year; for a 3-year energy payback, anything over 33% per year; for a 2-year energy payback, anything over 50% per year, etc: during the phase of rapid expansion, manufacturing energy consumption will exceed total generation.
This relationship is shown well in the chart in the abstract of the paper (note that this is a log-log graph):
Note that annual growth rates have risen at about the same rate as which energy payback times have decreased (the linking factor being the rapidly-declining costs of PV in the last 13 years: lower energy input -> cheaper panels -> higher deployment -> innovation in manufacturing -> lower energy input -> ...)