It's probably detecting Macrovision. Even if it is a tape you made, if there was some Macrovision protection on the source, it'll be on your copy. And so the combo player is programmed to stop if it detects that.

I'm just guessing here. I have a dual-deck VCR that does the same thing when going from deck to deck. Strangely my Nth generation bootleg copy of Pink Floyd The Wall Live had some sort of copy protection on it (which is probably why a pristine copy of that has never surfaced). To copy it I would connect RCA cables from the video out to the video in. The I would assign the the video out source to be Deck A and the record source for Deck B to be the video in that I had plugged into. This defeated the copy-protection detection and prevented the auto-stop.