Is anyone else's Windows 10 File History failing to update after the August/September updates?

Your report describes two different symptoms: a stale “last backup” display and modified files missing from recoverable versions. The second is the more important risk, because an unchanged timestamp alone does not prove that backups stopped. Make an independent copy of current files before testing, and preserve the existing File History drive and catalog. Create one new test document and modify another inside a backed-up library, then run File History manually. Open the restore interface and inspect whether both versions can actually be recovered; restore them to an alternative location so the originals are not overwritten. Record the file modification times, backup run time, Windows build, and installed update details. Since you already have a support investigation, add these reproducible results to that case. I cannot substantiate those updates as an officially confirmed regression or provide a release date for a fix; keep another backup until recovery tests succeed.