Synchronizers perform two functions-- engage the synchro in one direction and then lock one gear to the mainshaft.
Engage the synchro the other way and it disengages from the first gear, passes through a neutral position, and engages a gear on the other side.
If anyone is a tranny expert correct me if I'm wrong but wouldn't the vehicle have trouble staying in gear also if it was a sychronizer problem?
There may be some adjustment problem with the clutch and I have heard that transmission fluid that is not compatible can cause such problems also. Some people put automatic transmission fluid in a manual tranny which seems it would be too "thin" and slippery to me because I think of a manual transmission as being "thick" as gear oil should be.
My two cents says it could be caused by other things besides synchronizers.