Usually the tension of the take-up reel keeps the shut-off arm taught and everything works. If the shut off arm falls down, the recorder stops. Is that what's happening?

Inadaquate (or NO) take-up tension can cause this; so can WARPED take up reels. Another possibility: if you play a lot of old tapes, the groove in the shut-off arm collects dirt and oxide, so the tape - as it goes through it - jams, and the take-up reel can not overcome the tension. The arm "falls down" and shuts off the machine. Also SOME tapes (which were "cut down" from 2"
tapes) are poorly ****, and will jam some machines.

This is what I do for a living, so if these suggestions don't work, give me more information, and I'll solve your problem.