That's not the right question. Anyone can bill for anything they want to, and they can file any lawsuit they want to too, but whether it not it's valid and would be enforced by a court are different (and the right) questions.
So start with your written contract --what does it say about billing, like how frequent, how timely, whether bills not included on a timely basis can't be issued later on? I'm guessing they can bill whenever they like, and that there's some language in your contract like "no waiver of any right will be construed as a continuing waiver," which means that can always sue for something they neglected to enforce earlier.
ME provides for a 6 years statute of limitation for written contracts, and that's from date of breach, so I'm guessing they've got 6 years from the day you breached (didn't pay) to bill and to sue on debts. You're not likely to pay until you're billed, so the breach is after your payment is due, not from when the date the rental took place and when the billing should have happened. Since I don't know what your contract says, you need to review it to see what your rights are (and what their rights are). And with a long 6 year statute, you need to keep good records of your dealings with this company, especially now that you know they're not efficient in their billing.
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