Unlike a car clutch, the clutch pedal on a lawn
mower only relieves the tightness of the belt
driving the transmission pulley. I would suspect
that the one time in its life a tighter than normal
belt was used. Any dragging of the belt causes the
transmission to bind when shifting.

The scenario painted by corvetteguy has potential. Also suspect would be wear in linkages that result in the drive belt NOT going "slack enough" to prevent the transmission input pulley from turning when the "clutch pedal" is depressed. To help determine whether the problem is in the DRIVE BELT area, or if it is inside the transmission, do this: Next time the trans will not allow you to shift from one to the other direction......cut the engine off. If you can shift after the engine stops, your issue lies in the drive belt system. If you are still unable to shift after killing the engine, it's possible that one of the shafts in the transmission has gotten "twisted" (overtorqued or shock loaded at some time) and the gears or the "dogs" can't slide from one mesh, to the other. Also be sure to check any idler pulleys in the drive belt routing, a "dragging" or tight idler pulley bracket pivot shaft could be placing unwanted tension on the belt instead of letting the belt "go slack".
Check for missing return springs that could be broken or M.I.A. Sometimes, there will be multiple return springs at different places in a drive belt system. Finding an IPL of your machine would be a definite help in determining this. Or, you may just have to look for a hole or tab that "looks like" it had a spring attached at one time.
Also check the configuration and condition of the "belt keepers" or "belt guides" that are near the drive belt pulley on the engine crankshaft. These are supposed to be situated "close enough" to the belt pulley to prevent the drive belt from derailing or jumping off the drive pulley whenever the belt is slack. But, they should not be so close as to prevent the drive belt from shifting to a point of lesser contact during slack mode (whenever clutch is pushed down). Also, if the pulley on the engine crankshaft becomes rusted (inside the V-groove), that rust will sometimes afford enough "grit" to keep the belt spinning when it should be slipping. But, if rust were the case, that should disappear after a short period of use, and should not persist.

Thanks so much corvetteguy and mownie... I'm going to try what you suggested and see what happens. By the way, if the transmission is the culprit, is it feasible to save the mower? I've put a lot of work into it and it otherwise works well. Thanks again.

I've got a 22-year old MTD 38" deck with the vari-drive trans system, with forward, neutral, reverse. Mine has always done this when stopped up against a solid object (fence, tree, house), old belts or new. I just try to avoid getting into that situation....stop just before moving up against the object. Works for me.

This is a characteristic of our beloved Vari-Drive systems.

If your clutch when fully pressed down, is not completely "relaxing" the belt tension, then this characteristic can become more pronounced. Mownie above suggested things to check for that might be interferring with your belt becoming fully relaxed when you press in the clutch.

The shift lever moves a little shuttle gear back and forth in side the tranny. This shuttle gear has 3 big triangular 'teeth' on each side (they're shaped sort of like the nuclear radiation hazard symbol), and these 3 teeth mesh in with three similar shaped depressions on the inner sides of either the forward or reverse gear, depending on which direction you've moved the shift lever. (This verbal description would work better with a diagram, I know... still trying to learn how to stick pictures in here.)

When you stop up against something like a wall or a fence, tension pressure still exists between the drive gear and the shuttle gear, and this tension resists the shift lever trying to pull the shuttle gear free. Solutions are: slow down the motor to idle, exercise the clutch pedal back and forth several times, and even use body movements in the seat to relax that tension on the drive axle. If all else fails... turn off the motor, get off, and lift up some on the back axle. That will almost always free it. Best fix is just learn how to avoid getting the tractor stuck up against something like that... comes with practice.

As to your other question, it's not a defect, just a normal way these mechanisms work. Those of us here can tell you, these machines don't fail in small ways -- when they go out, they go out big .

I have a slightly different problem. When I shift into reverse the belt comes off. I have a 1988 MTD 38" 12 HP, 7speed. I replaced the belt as the seller advised.(I recently bought this used, and after using it a while, I regret this, but it was an Ebay purchase , and now I'm stuck with it).
If I'm really careful letting the clutch up it will occasionally go into reverse gear, but the "clutch" seems to grab very high, almost at full released pedal position. Is there any way I can adjust this, or is something else at fault? Any help will be greatly apreciated.

I have a 2000 yard machines automatic lawn tractor giving to me the trans is in forward it will not go in N or reverse I do not know a thing about it some one help please thank you