Did I max out Tactics Trainer?
New problems are being added all the time. Whether they can be added faster than you can solve them is another matter... :)
The reason you seem to have attempted more problems than exist, by the way, is probably because some problems are found to be faulty after they're added, and so get deleted. If you've attempted them before that happens, then they'll show up in your count of attempted problems, but not in the count of current problems.
It wouldn't be fair to repeat problems in rated mode, or somebody could just do the same problem over and over, getting the max rating.
At the risk of sounding like I'm trying to pick a fight, this isn't true. The user doesn't get to pick which problem they will try next. So you won't see the same problem again until after you've potentially attempted hundreds of other problems.
I am Very Pleased to report the following: Over the last 30 days, over 1600 problems have been made available to me on the Tactics Trainer!
THANK YOU CHESS.COM!! 
Amazing! I love Tactics Trainer, and it was the reason why I wanted a chess.com membership...tired to waiting for the next day to do three....
I just got a message on Tactics Trainer that reads "There are no more problems available at this time." & I can't do any more problems!
Will there be more tactics problems available to me in the future?
Or is that Chess.com's way of telling me to spend less time on the Tactics Trainer?
Has anyone else received this message?