In 1996, there was a publication by Greaves et al. in the Lancet titled "An air stewardess with puzzling diarrhoea" about a stewardess who presented with a 7-year history of abdominal pain and diarrhoea (up to 10 times a day). The cause they finally found was overuse of sorbitol-containing chewing gum. (Unfortunately the article can't be accessed for free)
There are more case reports like this, for example in the British Medical Journal where people consuming sorbitol in amounts of about 20-30 grams a day (one chewing gum stick contains about 1.25 g, apparently) had similar problems.
The authors conclude
that sorbitol consumption can cause
not only chronic diarrhoea and
functional bowel problems but also
considerable unintended weight loss
(about 20% of usual body weight).
Thus, the investigation of unexplained
weight loss should include detailed
dietary history with regard to foods
Lots of related links can be found here - it appears to be more frequent than I thought, even Vitamin C supplements containing sorbitol have been found as a cause of diarrhea...