I've now confirmed this with some MPEG 2.5 layer 3 files

• 16kb/s 11kHz CBR mono
• 16kb/s 11kHz CBR mono with VBR tag
• 8kb/s 8kHz CBR stereo

and in all cases I see the described behaviour. Additionally, the Seek Tool time does not agree with the music - it appears to be where the player thinks it is (i.e. where it would be if it had resumed from the right place) not where it actually is. So I don't think it's a matter of the player saving the wrong position, as would happen if buffered output was being lost. It's getting totally lost when seeking back to the correctly-saved position.

(That last one was pretty awful to listen to...}