I had a similar issue, but with a brand new deck which ruined some tapes and gave me an education on what stereo equipment just to stay away from. When I was 14 I was buying my first stereo from saved allowance and grass cutting. I had already bought a Pioneer SX-1300 receiver which is nothing special, but better than what most 14 year olds had at the time. I bought a Scott dubbing deck which I thought was a great deal because it had an auto reverse deck and dual dolby.
The first one I bought had some serious speed issue as if it had a binding belt so I took it back, but the second one which seemed to be fine would eat the tape but only on the beginning of side B on the recording, non auto reverse deck. This problem baffled me since it was never side A. As it turned out, the deck was actually messing the tape up via a misshapen pinch roller on the initial play though on side A. The tape was messed up enough that it would mistrack once side B was started. Luckily this deck went back and I got refund since I did not want another dud and I was appalled at the fact that Scott, then owned by Emerson used one drive motor to supply two decks. I bought a JVC for slightly more that was very reliable.
Basically what I am saying is you need to replace that pinch roller if you can as that is the culprit. I don't know how it got so misshapen unless it has lots of hours on it from a previous owner or in the case of my father with a Sanyo cassette deck in his 1981 Chevy Citation X11, put the wrong fluid on the pinch roller to cause it to harden up, thus eat the tape. Oddly enough this now helps me figure out why his Concord F-400 ate tapes and mine didn't.
