What are the specs of that beast? I assume you're either using a PPC-card or that you aren't browsing the web much. 
PPC card, 030 or 060 are pretty much the same for browsing the internet.
The problem comes from outdated browsers (Ibrowse, AWeb) rather than CPU.
Anyway, i can say my A1200 gets almost as much up time as my laptop Toshiba Win 7 these days.
And of course i browse the web with it, but that's limited to amiga related sites and amiga forums.