Okay, I've got my lathe reassembled and also discovered a few problems leading to the slippage. The overall issue is too much friction. Here is what I did to reduce friction enough to get the threading working and also a quick but dirty way to create more friction at the "elbow joint" where the 2 arms that hold the gear train in place join. These are called the "Primary Support Shaft" and "Secondary Support Shaft" in the Sherline documenation. They are held at the desired angle by a 10-32 socket head bolt that threads into the primary support shaft.
1. There was some friction inside the leadscrew support that houses the pieces that engage/disengage the threading action (fixed shaft and sliding shaft) due to some burrs I cleaned off the burrs, cleaned and regreased with silicon grease. Leadscrew was cleaned and relubricated as well. There were also some wear spots on the fixed shaft, so I lightly filed them because they seemed to be rubbing a bit inside the support. Once deburred, cleaned and relubed, the shafts rotated nicely inside the support.
2. The gib strip for the saddle was cleaned, relubricated, and backed off a bit to decrease the pressure it was applying.
3. The bushing that holds the 40 tooth gear (Gear E in the Sherline documentation) had a rough surface that the gear rotates on. It looked a bit like galling. I cleaned and lubricated.
3. Leaving the gear train in the arms, I detached the assembly from the lathe and spun the gears. The 40 tooth gear (gear E) had an area of about 4 or 5 teeth where it would catch with it's neighboring 20 tooth gear (Gear C). The same location on the 20 tooth gear seemed fine on the other side of the 40 tooth gear during rotation, so I am assuming the 40 tooth gear has some tooth shape issues. The teeth may be too thick at some elevation within the tooth. There was also some funny wear in this area. The engagement of this area when everything is put back on the lathe is the area that causes the arm to move, disengaging the gears. As a sanity check, I replaced the 40 tooth gear with a 36 tooth gear and found that it worked fine.
4. I put the 20 tpi gear train back on the lathe and rotated it both directions for a bit. It seemed to be working fine, but finally failed once again. I tightened the bolt holding the arms together a bit more and added a small 1" C-clamp near the screw to apply more pressure without over tightening the bolt. It is now working without failure. I can still feel a bit of periodic friction in the system, so I need to look at the 40 tooth gear some more for a more thorough fix. It could be that my current setup will simply wear the other gears out in time. I like the idea of using a locking bolt too that was offered. I'll give that a try too.
I checked the flatness of the arms and found that the secondary shaft (the one on the outside, away from the headstock) does have a bit of a bend in it. It bends about 0.003" over 1.5", so the angle change is very small. It could be a contributor to the the gear meshing issue, but it seems like there is more play in the system than the angular change due to the out of flatness. The surfaces of the arms that are engaged when bolted together appears to be flat.
I'll give the factory a call about the gear. They may know about some issue and have a fix.
Oh, this is a bit off subject, but I discovered why the thread stripped on my base t0 leadscrew support attachment. Sherline used a 3/8" long 10-32 socket head bolt to attach the base to the support. Sometimes there is an added spacer, which my lathe uses. Once you add the space, lockwasher and thickness of the base and support metal, there are only a couple of threads on a 3/8" long bolt. The fixed shaft has a groove in it and is held in place by the screw. I found that a length a bit less than .470 would pass through all the pieces and hold the shft in place, so I ground down a .5 long socket head bolt to size and used that. I also replaced the bolt holding the leadscrew thrust on the other end with a longer bolt because it appeared not all threads were engaged at that end as well.
Thanks for the ideas! It's great to have other brains thinking about a problem and also hearing other experiences when trying to come up with a solution to a problem. Sully, I hope something here helps out your slippage. I'd be interested to know if something helps or not.