Hi Bernie
I have exactly the same problem. This is the first time I refreshed my test managed systems since I've been on solman 7.1 SP10 and I got the exact same "No RFC for system <SID> client nnn" plus " Name or password is incorrect (repeat logon)". So yes, this strange RFC maintenance behavior looked to have been introduced with SP10 [before I was on SP07 and I didn't have the issue]
Just like you i think i also have a good understanding of how solman works but this time I'm very much stuck!
I haven't seen an OSS note with that problem symptom so far....
Have you managed to solve your problem or did you end up opening an incident with SAP?
Thanks and best regards
Francois