317 starter disengages?

I had a similar experience a few years ago. The starter drive has a rubber disk inside that acts as a slip clutch or cushion. It gets worn to the point that it slips too much. The replacement cost (Deere) was terribly high at the time, about 2/3 cost of a complete starter.
I used a 3/4 drive socket that had a chamfer or bevel that fit the crimped end just right. Smacked it with a hammer until it tightened up. Pretty crude, but it has worked OK since then. The starter also needed new bushings and a good cleaning.
There may be other reasons for the problem, such as the rubber getting "oiled" from an engine leak or something. You will have to at least unbolt the engine and raise it to remove the starter. Still tight quarters as I recall.
Good luck, hope you find a fix.

tommyhawk

OK, if the starter drive gear just spins and doesn't actually engage the flywheel ring gear, it could be a low battery, bad connections at the battery, engine ground, or possibly the solenoid.
Could be (very common) a lack of lubrication at the area where the starter drive slides on the armature shaft.
Sometimes it gets dirty and gummed up and just won't move correctly on the shaft. Cold weather aggravates this situation. If this is the case, you might be able to get the engine tin loose enough to spray the gear end with a light lubricating oil such as WD40. Most people recommend graphite powder as a permanent lube as it doesn't attract dust and dirt as oil will.
In the first response, I forgot to mention the squealing sound with slippage. Also the bur-r-r-p sound of the dry worn bushings. You didn't have that, did you?

tommyhawk

Adam, I'm sure the best solution would be to pull the starter and give it a good going over, if you have the time and a warm cozy place to do it.
Otherwise, once the battery and connections have been eliminated, try to free it up with some WD40 or something similar. Just avoid soaking the "clutch" area. If that works, that could get you by until Spring. Don't have to worry much about dirt and dust in the snow!
BTW, my experience is only with a Series I. Don't know if the starters are the same, but suspect they are.

tommyhawk