Many higher end cassette decks use low torque drives as a means of
lowering the wow and flutter specs.
The manufacturers intention was that only high quality cassette
should be used. i.e. ones with only the lowest friction ratings.
I have and older Nakamichi and a top end Akai that are like this and
are particular as hell about the quality of cassettes run in them.
I usually had best results with Denon tapes or the pro stuff put out
by Loranger industries. Both had high quality bearing mechanisms in
the cassette hubs as well as really good graphite pads in the shells.
If you eliminate the tape drive as the problem take a look at the
condition of the cassettes.(Use the sharpened end of a regular pencil
inserted into the drive hubs of the cassette. If any drag is felt when
rotating the pencil you'll need to replace the graphite pads in the
shell.)

Just what I was saying... New cassettes work fine. I am trying to play some
older cassettes in order to transcribe them to other media. I'll follow up
the other fellow's suggestion that the pinch roller pressure may be
insufficient. I'll also see what triggers the auto-stop and whether
something is making it stop prematurely.