Recourse for what? If all they're doing is saying, "You owe us a month's rent", you can respond, "No, I don't."
As a general rule, an ambiguity in a contract is construed in favor of the party who did not draft the contract. Unless they can point to something in the surrounding discussion or communication that would suggest that the intent was to enter into a 13 month contract, I suspect they would have a hard time convincing a court that this was intended to be a 13 month contract. You say that the last two leases are for thirteen months - if the second-last lease was also for "March 1st, 2010 to March 31st, 2011" and they had you sign a new lease effective March 1, 2011, that suggests that even they thought the prior lease was for twelve months.

