Hello there,
My Mum is suffering the same problem with her BDP3000 and a Samsung screen(LE37B652t4w), It goes blank for a few seconds and picks up where it stopped. This is most annoying I have tried different HDMI leads, different channels on the TV, updated to the latest firmware, but to no avail sadly.
Watching Sherlock Holmes BD it stopped three times in eight minutes, which is frustating this appears to be getting worse as the player gets older.

As previously mentioned in this thread it has been mentioned about the player running out of memory would a flashdrive being plugged help this solve this problem ?

This player is not connected to the internet