Broken hyperlinks "solved".
After reading HarryT's 8/10/2009 thread "Broken hyperlinks" [resurrected by mrevent on 6/21/2011], at least I know I'm not alone.
I "solved" the broken hyperlink problem by figuring out what Sigil did to break the links, then editing every last one of them. At least I could do this within Sigil -- it didn't break them a second time.
Seems like I'm talking to myself here ...