Here is what I got from tech support...
"It turns out that there was a temporary service disruption on services2.arcgis.com that affected replica creation for Hosted Feature Services. This issue has now been resolved and all services should be functioning normally again."
I can download my hosted maps again, but I worry that this system isn't as stable as I thought it was, so I'm keeping a backup on server for now just to make sure our disconnected field crews have something to record data in during their extended field surveys this summer.