The ring gear has gotten chewed up over time, and now
will sometimes not disengage while the starter is rolling it over.

The Lycoming starter drive is supposed to lock in the engaged
position until the engine starts and the RPM comes up somewhat. There
are centrifugally-released locks in the drive itself. Some pilots get
all concerned about the drive "sticking" in the engaged position, which
can cause grinding and ratcheting noises when the prop is moved, but
it's normal. Anytime a start has been attempted without the engine
catching will result in this engagement.
The chewed-up gear teeth often coincide with the prop's stopping
position. Check and see if the teeth in the two prop-stop places are
the worn ones. Moving the prop a little (backwards!) before startup
will place less-worn ones in the engaging position.

Dan