Why does the iPhone's iPod app sometimes forget playback position?
This could be a memory issue that the developer was forced to handle this way. All apps in iOS are subject to memory warnings at which point the app (developer) is to free up as much memory as it can by clearing out what the developer considered unnecessary information. 

Another point of of possible quitting is if a phone call is being received. Apps only have a split second to save what is crucial before quitting to make room for the call. Again, the developer has to decide what is truly important and what isn't to save.

The save position may not sound like a lot, but mobile devices really don't give developers a lot of room to play with and media of any type is a resource hog.