Same issue here, Avast Web Shield went down (Windows 7, 64 bit) as soon as the last program update 7.0.1474 became available and was detected by Avast (so Web Shield was down even before updating the program and choosing Update didn't fix it).
In my case, I fixed it by restarting the Avast service using Windows 7 "Control Panel" and "Service". I needed to do this twice, once under my "Administrator account", which still didn't solve the issue under a "Limited rights account". I solved the issue under Limited rights account by first logging in under this limited account, and than right clicking the Services option in Control Panel, and choosing "Run as Administrator". Once I restarted the service once again using this "Run as Administrator" under limited account, the Web Shield came back on there too.
Please note you may get a Windows error warning "that the service didn't stop properly". I had forgotten to close the Avast program window before stopping the service. Seems Avast is actually quite robust here when knocking the service from under it's feet, it simply asked first if I wanted to stop the service (I clicked Yes), and than Windows came up with the error warning but showed in the Services panel the Avast service was stopped. When I restarted it, Avast program windows came immediately up again showing Web Shield was now properly on, as all other shields.
Good to hear the Avast team may have tracked down and fixed the urgent issue!