There really shouldn't be any reason for it to change/erase them, I'm at a loss as to why this would be happening.
DavidR, thank you for your candor. I'm not even familiar enough with the different areas of Avast to say which one this falls under. It could be general registry settings protection (which I had thought Avast doesn't do). It's possible this is extra precautions applied to general Internet Explorer options (as the proxy settings are part of the same set of controls that govern homepages and other IE settings).
For reference sake, the exact set of registry keys it's reverting are under
HKCU\Software\Microsoft\Windows\CurrentVersion\Internet Settings\If you don't have the slightest clue, go found out.
Test things.
Eddy, that response is staggeringly useless (and in my opinion extremely arrogant, as well). You may as well have replied "Figure it out yourself, chump." Without even a starting point, testing things from scratch will take hours if not days of my time -- time which I would honestly much rather spend with my family. Reverting my proxy registry settings appears to happen at random irregular intervals (from as little as 5 minutes to as long as several hours between occurrences). Testing blindly means turning off components and waiting an unknown amount of time and hoping enough time has passed that if it was going to happen it would have.
A more useful response would be like DavidR's, something along the lines of: "I don't know why it's doing this, but changing registry settings sounds to me like it's related to the File System, so try starting with disabling the File System Shield and see if that works."
(For what it's worth, I have tried disabling the Web Shield, because that sounded like the best bet to me to start with, but that didn't prevent changing my proxy settings. The File System seems like my next best bet, but even if that was the solution I see no sub-setting in that Shield that would prevent this from happening, nor any way to set exclusions that target the registry. I see the File System Shield as the single most important component to successful anti-virus, so disabling it entirely is not a long-term solution.)
I realize that by only using the Free version the only avenues I have open to me are the KnowledgeBase and community support here, but if Eddy's response is typical of the level of "community support" that Avast engenders, I certainly won't ever be upgrading to a paid version, and would honestly likely choose some other antivirus vendor entirely.