From what I've read the potential problem is that putting the yeast through a round of fermentation can change them so that what you are using the 2nd go-round isn't really identical to what you were using the first time.
So far I've only thought of one specific example of what could be happening and they are called "petite" mutants. It goes something like this: you pitch healthy new yeast into a batch and they take off quickly because they can use O2 that is in the wort that lets them grow faster. (this is why we go through the trouble of aerating our wort before pitching the yeast)
The O2 gets depleted quickly as the yeast proliferate, and the bulk of fermentation kicks in. However, the absence of O2 allows a specific type of mutant, called a "petite" mutant, to flourish. Petite yeast have lost the ability to use O2. Normally this is tough luck for the poor sickly petite mutant, but its not a big deal in your fermenter since there isn't any O2 around anyway so the petites probably work just fine during fermentation. Come the end of fermentation, our yeast cakes probably have quite a few of these petites in it. So, if you pitch gobs of these into a new aerated wort (has O2 again), you would probably get a slower start on your fermentation since the petites can't use the O2.
Obviously, people have been re-using strains though, so there are ways around this - I'm just not sure what the tricks are. The Palmer book mentioned something about trying to get the yeast from the middle of the cake - maybe this enriches for the normal yeasties.
The other problem I've seen mentioned is stress from high alcohol content, but I don't really get what the problem is for the actual survivors.