What could cause a rear tine tiller to disengage the tines when the tine shaft shear pins are not broke.

Two possibilities. Something has jammed the tines.
Pull the spark plug wire off and tuck it away someplace so as not to touch the plug.
Tip the tiller up and examine the tines for obstacle such as a rock. If there is nothing jammed try to turn the tines by hand. If the they turn freely you most likely broke a shear pin that secures the tines to the axle.Clean the axle and tines and examine very closely for the pin.
If sheared ( broken) you will need to drive the broken piece out and replace the pin.
There may also be a problem in the transmission case. You would need to remove the tines and case to open it

most tillers are equipped with a shear pin down by the tines. for this reason. if you hit something it will shear the pin and not do damage to your machine. it don't sound like that happened here. make sure the tines are disengaged. if the rope wont pull it may have sheared the flywheel key. there are videos on you tube that will show you how to take off the cover, the flywheel and check to see if this has happened. it may have locked the engine up at the worst scenario.

if we are speaking about the shear pins on the tines, the ground is the problem and you need to begin your first pass on a more shallow setting and progress to a deeper setting gradually. if we are speaking about the shear pins on the tires w/o engaging the tines then these should not be breaking and I recommend that the tiller be examined by an authorized dealer.

It appears that the gear case on your model is not capable of being serviced. The cost is over 300 dollars. There is a shear pin or similar connection in the case where the shaft connects to the pulleys. It has broken off and the shaft has no torque now.

Yes, there are shear pins on the tines and on the wheels. Can you check to see if the belt actually moves when the pulleys turn?

belt worn and too loose, maybe pulley slipping on the shaft, shear bolts or pins broke on tines. worse case sheared key in tranny case for drive gears.

You might have just sheared a shear pin that's how some of those are designed. Check around the shaft area that connects to the engine you might find that a pin is sheared if so, pound out and replace. Sometimes also called shear bolts. Good Luck...

Yes there will be a shear pin
It may also have an engagement cable adjustment issue

It sounds like the key that holds the pulley on the front of the tiller transfer case has sheared into. Carefully remove the belt safety cover so the belts are exposed and start the tiller. With a flashlight look at the pully on the lower shaft and shaft area. Carefully engage the tines and see it they are turning. With a second person visually, from the side, inspect the pulleys to make sure they are turning. Now carefully load the tines and see if the pullies of shaft stop turning. If the shaft stops and the pulleys keep turning then the key on the shaft has sheared off. If both keep turning then you have something that has broken or sheered in the transfer case. This type of inspection is dangerous and needs to be done at a distance with a flashlight so you can see down in the shaft area when standing off to the side while someone loads the tines. It is very difficult to try and see if the shaft is sheered in the pully as is the case without the engine running. The key has friction and it is difficult to turn the tines with the drive engaged to the engine. The only other option is to disassemble the transfer case to see what has gone bad. Please be careful testing it. Good Luck, RAC