Sometimes, I can't access any websites at all; SheepShaver just dies saying "Segmentation fault". This is with "Ignore illegal memory accesses" turned on. With it turned off, it always dies with a segmentation fault when I try to access a website. It does this in Netscape 4 and iCab.
It totally crashes for me when I boot using slirp. It runs fine until I try to use networking, then it crashes. It'll even crash opening up the TCP/IP control panel if it's using slirp.
slirp networking is known to be not very robust, but I never heard of crashes when doing nothing but opening TCP/IP control panel. You can try removing TCP/IP preferences from the Preferences folder in System Folder and launch SheepShaver again. Then make sure the control panel is set to Ethernet and DHCP.