It's a matter of location, location, location. Sadly, most of the methods we use for extra-solar planet detection don't work within our own solar system.
One of the primary ways we have detected planets around other stars is by gravitational tugging. This method of detection will be more prone to discover large planets that are close to the sun which they orbit. Our instruments are only sensitive to a degree that will allow us to detect a Doppler shift in the motion of the main star.
The other method for detecting planets is a transit method. This means a planet needs to pass between a star it orbits, and us. Obviously Tyche will not do this.
As for detecting a planet that could be anywhere from the Kuiper Belt to the Oort Cloud is a huge amount of space to cover (even given a relative distance of 0.25 light years away). Observation time on a telescope is not an automatic right given to anyone who wants to use it. And given the rather tenuous data on this supposed planet, most astronomers would most likely select to observe something else instead of going on what may appear to be a fruitless search.
Not to say that some are not looking for it. There is something about finding a planet that tends to put people in history books, and astronomers are human beings too. I'm sure some would relish the idea of finding one.
Dr. Phil Plait had a few things to say about this purported discovery:
Let me be clear: while certainly possible, this idea is not at all proven, and in my opinion still pretty unlikely. As usual, this started as a more-or-less accurate media story and is getting inflated as it gets re-reported. As far as I can tell, the original report was in the UK paper The Independent.
Here’s the deal. Two astronomers, John Matese and Dan Whitmire, have theorized about the possibility of a previously-undiscovered planet way beyond Pluto for some time. This is not a crazy idea; we see planets orbiting other stars way out, and there’s other evidence big planets can be pretty far out from the Sun (mind you, evidence does not mean proof). As it happens, there are lots of chunks of ice orbiting the Sun pretty far out as well. Some of these have orbits which bring them into the inner solar system, and we see them as long-period comets.
What Matese and Whitmire did was wonder how a big planet would affect the orbits of these comets. If you measured enough of them, would you see the effects of the gravity of this planet? They claim you can, and even gave the planet a tentative name: Tyche.
I read their papers, and thought the data were interesting but unconvincing. The sample size was too small. A bigger study was done, but again the effects weren’t quite enough to rise to the level of breakthrough. I’m not saying the astronomers are wrong — the data were certainly provocative, and potentially correct! Just not firm enough.