I wonder if the person in charge of the club has a rank. Personally I would not train under someone whose skills have not been recognised by other martial artists.
It may be that the person in charge is not a black belt yet. If this is the case then they can't award belts. In many cases it also means that they can't have insurance. I would definitely check this. No insurance means trainig at your own risk.
However, good Aikido is a lot more important than a belt, so if their Aikido is good and they choose not to grade others, then it should be OK, if you like that particular club.
Just try to find out why they choose not to grade.