Is it avast! 4.8 or 5.0 you've installed?
I have previously installed 4.8 with Pentium Pro and other non-MMX processors without problem.
I doubt very much that lack of MMX instruction capability is causing your P133 to restart.
It's more likely to be the P133 overheating or unstable motherboard voltage. The Centaur/IDT 200MMX is a curiosity to most people these days but a little gem nonetheless.
It's extremely cool running and core voltage variation tolerant (2.4 to 3.1 from memory) and while it is MMX compatible, the core hardware processes only the most common W95 instructions. Less common instructions, especially those from NT/2000, are done by software emulation.