sorry for a long delay.
this is very strange situation, because it can't be problem either only of R4 or only your system, i think one affects another. this remark unlikely helps you a lot
i think, it can be consequence of running programs (video & R4 played simultaneously with mysterious multiscreen overlay settings for example, and maybe some decompressors settings if you use VIDPLAY module), or incorrect R4 system settings, but it usually fixes by reinstalling R4.
also, it can be internal problem of R4 if you have your complex and intricated custom scenes. i faced the similar.. try to play with R4 settings - find prerfs.txt file and change gl/pbuffer ( 0 for ati radeons and 1 for nvidia cards as my experience tolds me), gl/pbuffer/height and gl/pbuffer/width - 1024x512 if you run R4 in 1024x768 pix, or 512x512 for better performanse and quality losses (losses increases if you use few overlays at the same time), gl/prerendertex must be 0, do not ask me why
but try to change it and see what happens.. hope, this helps a little..