I have the same problem, and I was already wondering if it was just my system, since I could not find any information about this online, either here or through Google. But in my case it's been weeks if not a few months since it first happened, I am not really sure. At first I thought some virus was constantly shutting down Avast, but I scanned the computer with my laptop (over network, it also runs avast, and there it still works, the laptop runs Vista 32), with TrendMicro Housecall, with Superantispyware, and GMER and none of them found anything more than a few tracking cookies. Then I did the uninstall-reboot-install-reboot-update cycle, but that did not help either.
Currently, like mojo mon says, the splash screen stops working when I try to manually start Avast through system tray, or when I try to manually scan a file or folder through the shell. However, resident protection, and scanning downloaded files (through Firefox) still seems to work normally. I'm using the latest Home version of Avast, I am not at home right now, but I'll post the version number later. I am also running Vista 64, on a 7-month old system with a E8400 processor, 4GB ram and Vista SP1 installed and fully updated. I have not tried doing anything with DEP.