Can you test:
Have a GB cartridge in, suspend a tournament using the imported team, then actually use that cartridge to play GB pokemon and save to force a data change, and see if you can still continue the tourney. Possibly feed one of your team a rare candy or something to force a data change. See if that breaks it and prevents resuming. I would assume that when the GB saves, it might overwrite something that Stadium placed on the cartridge? Either that or data mismatch forces it to be invalid.
Either way, if you use the cartridge to play and save some GB pokemon, you'll probably lose the suspended tourney. Alternatively, it may be a general warning against any change to save data at all. So try moving Pokemon around with organize, or use the GB option to play pokemon on the n64 and save?
Just a guess though.