It's reasonable to infer that the lawyer's argument is that the statute of limitations started to run on any individual rent payment when that payment was due, such that the statute has run for any rent payments due more than three years before you filed your lawsuit, limiting you to rent claims for @October 2013-July 2014. If they owed more than @10 months rent at the time they finally moved out, you made a novice landlord's mistake -- you have to be hard-hearted when tenants come to you with excuses about why their rent is late, because if you don't... this is what happens. I would not be surprised if they presently have a legal aid attorney who is helping them for free.
If they are claiming that their more recent payments were for the more recent rent charges, and not for the arrears, you can argue to the court that any money you received was first applied to back rent and not to the most recent rent debt. You can also try arguing that the rent should be treated in the manner of an open account, rather than a series of separate obligations, such that the statute of limitations should start to run at the time the tenant vacated -- I can't promise that the court will be receptive to the argument, but if the court accepts it then the entire debt should be collectable.
If the lawyer has filed an actual motion, you can tell us what the lawyer's arguments are.

