Drink a little at a time the refill with tea and leave it on the counter. Wait a few days and drink. Then as you lose tea, just refill and the process continues indefinitely.
My wife uses half gallon mason jars for hers. They are cheap to get a case of them at wal-mart (less than 20 bucks for 6 of them) and have plenty of other uses too. They have a reasonable footprint to work around in the fridge. She bought the one piece plastic lids for them too.
I think she starts with 2 gallons, dumps 1 gallon into the half gallon jars and adds another gallon of tea back to the fermentor.