After doing some digging, my conclusion is that the limit does not reset. However, I was told by a customer service associate at the Department of Education that the financial aid office of your school supposedly is the one that tallies the aggregate loan number. It might be possible to have the number reduced or removed if you show proof of payoff.
Personally, I kind of doubt that explanation and think that the lifetime limit is likely a hard limit. One thing that might give you some leverage is the amount of aid available with different student statuses. For example, if you were considered a "dependent" student while you did your undergraduate program (were under 24, not homeless) and are 24 or older now, your lifetime limit should actually be $26,500 higher now. This might be a way to get some more money toward your education.