I am no expert, but I will throw in my thoughts.
I know my Amiga 1200 did this when I had the 030/50 Microbotics accelerator...At times it mysteriously locks up... I found out the memory in it was turning bad because I notices the gfx becoming corrupt for no reason, but when I put in a spare 32mb simm I had, the amiga worked nicely. No lockups or slowdown or corrupted gfx.
What is your current amiga hardware setup?