What causes my left CV joint to pop out from the
diff? what are possible problems?
That needs to be looked at closely. Need to inspect the stub end (input shaft) for any wear, especially around the retainer ring, ( "C") clip, There should be no play in the input shaft going into the differential. The shaft should snap into place, may just need a new retainer ring, ("C") clip on the shaft. Another cause would be a bad bearing in the differential allowing play, which would work the input shaft loose, to come out.