I'm gonna go against the grain here and say that yes, it does but only a small amount. I think that if the beer has yeast in it, it can continue to eat away at the sugars very very slowly.
As an example, I brewed a Barley Wine in late 2009. I racked it to secondary after 67 days in primary and took a gravity reading at that time, which was 1.018. By 67 days, the beer was obviously very done. No visible activity at all, pretty clear.
I then left that beer in secondary for 372 days. I just wasn't that happy with the beer so left it there (it's a lot better now and I'll bottle it sometime in the spring). I recently needed to rack it again to make room in that particular demijohn (it was about 14 liters in a 20 liter demijohn, so racked it into a 15 liter one to make room in the 20 liter one for another strong beer's secondary). The gravity had dropped a further 2 points to 1.016 in that time in secondary. Not a lot, but it did happen.
Furthermore, when I was at a tasting at the Great British Beer Festival in August, we were tasting Fuller's Vintage Ale with their rep, a guy who's worked there for 30 years and knows his beer. He said that that beer does slowly increase in strength over years as it ages as the yeast eats away at the sugars.
Anyway, them's my 2 cents. I don't think it amounts to much of an increase but I think it does happen.