Model AV-48WP55, approx 3 1/2 years old. It has manual 81-point convergence. It seems like I have to do the convergence almost everytime I view it now.

Is there some reason the convergence keeps getting misaligned?

You're letting it warm up for 30 min before checking/adjusting? How far out is it? Start looking to replace the IC's. http://www.hometheatershack.com/forums/manufacturers-service-support/5600-crt-based-rptv-convergence-repairs.html

I always let it warm up fully before checking. Now, I may be anal here, but were talking about very minor movement. I guess my question is why there should be any movement at all once the convergence is set. The tv is not moved or touched.

Electronics drift with age and especially with heat. A warmup period should be one hour (give or take), not 10 minutes.
The older it gets, the worst the problem will get. That's the main reason I don't miss CRTs'.