can you be more specific on which belt you speak of?

and also just fyi...
when dealing with 'recertified' machines you are 'trusting' that the dealer went through the machine thoroughly and did replace all worn parts. Sometimes they may not replace every single part on the truck if it appears to be satisfactory according to wear standards. It could have been within the spec's they use and at the time it was ok. But being you've only had it a month and this part broke i'd be willing to say it may of had a problem that was not visible at the time of inspection or they just simply overlooked it.