Hopefully someone will post who knows more about this stuff, but what I would suggest is that you get out from under them as soon as possible.
Besides finishing the contract and paying the remaining payments on schedule, there are a couple of other avenues to explore.
If you have the funds, you could pay off the car and be done. You'd likely save some interest too. Be sure to call them for the payout amount and get it in writing in case they try to burn you later.
If you don't have the funds, you might be able to refinance your loan with another lender. If credit is an issue, perhaps a co-signer would help.
If you're stuck though, which many people are these days, just keep on going as best you can. Remember to keep good records of when you made your payments and how much you paid. Unfortunately, you're just a number to these clowns and are only as good as your last payment.
If they can't seem to handle online pays, I'd stick to mailing them a check or doing a debit/credit card over the phone. Either way, follow up with your bank after you make each payment so you can be sure that they got it and took the payment. That way you won't fall into any of those 'held' payment scams I read about so often.
good luck