The Short Term Rental situation isn't entirely different from the plight of "public easements" retained on discontinued town roads, the similarity being use by others who have no long term stake in the condition of the road. They are therefore likely to come, abuse it, and leave, while those who live there and depend on the road for access are left paying the bill for repairs. At least in the case of STR's, there is someone identifiable who has a responsibility to the road (i.e. the owner of the rental property) and they should be able to identify who the renter was who caused the damage. But where the owner of the business is not present, they are unlikely to see the damage and it may be difficult to convince them that their renter did in fact damage the road.
I would recommend taking pictures of the road at regular intervals so you have some proof of deterioration at any particular time. If you can catch the guilty party on a trail camera, (doing donuts in the gravel road with an ATV, for example,) that's even better. Or take a video tracing the ATV tracks back to where the ATV's are parked. (I'm just using ATV's as an example, as we've had d trouble with them. There could be other kinds of damage.)
I can think of a few possible remedies, most of which should appear as an amendment to your bylaws, or, if you don't have bylaws, in a written "formula" for assessments.
1) The Statute allows a lot of flexibility in how you determine your "formula" for assessments. As long as everyone in the same group is treated the same, that has been considered "fair and equitable" by the courts. So you could specify in your formula that year-round residents pay at one rate, seasonal residents pay at that same rate or at a different rate, and rental businesses pay at a higher rate because of the associated risk to the condition of the road. If the rental business objects, tell them they can just pass the cost along to the renters.
2) Require a damage deposit. At the end of the year if there has been no significant damage, the deposit can be returned, or rolled over to the next year.
3) Specify that anyone who causes damage to the road, or whose invitees cause damage to the road, will be billed for the repairs.
4) When you notify the owner of the rental business of your new policy, suggest that they put something into their rental contract to put the renter on notice. For example, the rental contract could require a damage deposit (although some may take this as license to damage the road because they have already paid for it.) Or the contract could specify the renter may be charged an extra fee if they damage the road. Or the rental contract could specify no ATV use on the association's road, or ATV use limited to 5 mph strictly enforced. Or the business owner could be asked not to rent the property during March or April, or be told that if they do rent it during mud season and damage results, they will we charged for repairs, so they should charge more for rentals during mud season.