Yeah, that doesn't make sense to me at all. I've owned MacDive for so many years that I can't even remember the registration process. If I remember correctly, you're sent a license file that you apply to the software. But I definitely remember it being a set-it-and-forget-it situation. Sounds like maybe something got messed up when you initially applied the license. So, I see no reason why it won't work for now on.
I also want to make sure you're not doubling your efforts here with downloading/syncing. You said when you were on your trip you downloaded the dives from your Teric to MacDive on your iPhone? If so, I just want to make sure you're not also downloading the dives from the Teric to your Mac. Once they're on your iPhone, all you have to do is sync them from the iPhone and then open up MacDive on your Mac and click Sync and they'll come down. Of course make sure they're both initially set to sync via the same service. I use iCloud. Once that's set it's also a set-it-and-forget-it thing.