Basically, Avast’s port-scanner protection has been disabling my access to my networked Brother printer. I have checked Avast’s logs, and this is indeed the feature that is causing this issue.
Short of disabling port-scanner protection, is there any way I can specify that connection attempts from the printer are to always be allowed?
Huh, I didn’t think that a clean install would help (you know the typical Microsoft “reinstall Windows” joke :-/ ), but after uninstalling it, and also running the separate uninstall executable, rebooting, reinstalling from scratch, it appears to be working now.
I also reinstalled only a minimal set of features (just the ones I use the most, including the firewall), so that might have done something.