Okay, so on the "Upgrade Account" page, it says that diamond members get unlimited access to everything, including the Tactics Trainer. This looks like a problem that you should report to Chess.com right now, so you aren't wasting money on your diamond membership and so Chess.com can fix this to prevent this from happening to anyone else. I think this should be dealt with soon, so I would suggest you going through this link, to Contact Help and Support:
http://support.chess.com/Tickets/Submit
If this is your first subscription to a diamond membership and it has been less than 31 days since you ordered the subscription, then you can always refund the membership. If you want the FAQ about refunding, I can get it. The FAQ also includes the link to refund a membership. I hope I helped!
-BlueGator456
For a while I've been having an issue with the Tactics Trainer on my Android devices. I can attempt quite a few problems per day, maybe 25 or so, before I get the "Daily Limit Exceeded" dialog. I've attempted logout/login and that did not help.
This problem exhibits in both my Android phone (2.3 Nexus S) and tablet (Honeycomb Asus Transformer).
I really only maintain diamond status to have unlimited access to the tactics trainer, so this is a high priority issue for me.