Infopath cannot save the following form. this document library was either renamed or deleted or network problems are preventing the file from being saved
You retry - problem persists! Assuming you don't actually have network issues, the problem is likely that either (a) you didn't install the Desktop Experience (I know, I know) and/or (b) the Windows Themes service isn't running. Turns out, InfoPath needs the D.E. features and that service to work.
In most cases, it will be (a). You can use the system manager to install quickly but you can easily do it from PowerShell:
The command (in case you can't read it) is:
As noted, once complete, you will have to reboot the server. IF this doesn't work, check the Windows Themes service (it should be set to Automatic and should be started).
Kudos to David Lean on this.