Well, duh. I should have mentioned all of that. Sorry.
I am not running an ancient version of Retrospect - in fact I am running 16.6 on Windows 10 Pro.
I did take a look at the volumes database and cleaned it up since it seems that the failures with trying to connect to the new backup target left some clutter in there. That, however, did not solve the problem. Regarding the not accessible message - no error code - it's in a popup. However, the operations log does show a message "TVol::Set: no volume name" which makes me think that the volume isn't accessible because the particular piece of code that adds members to existing backup sets neglected to pass that information to the piece of code that actually sets it up. It only seems to happen with UNC specified volumes. I can add local disks all day and no problems.
Right now, I'm thinking that this is yet another bug that was added when 16.0 came out. I've got two tickets open for serious problems with the storage group feature that have been open since March! They've admitted that one is a major design flaw, and they were working with me on the other problem for a while and then stopped just saying that it had been sent to Engineering.
My confidence in the product is pretty low right now. I've had to do a crazy number of catalog rebuilds on the NAS backup set since 16.0 came out due to crashes. And, if they fix the 16.0 problems in 17.0, I'll get to pay for the fixes!!