Re: My Right-Of-Way Rights to My Landlocked Land -- What is Code
One important thing you need to find out: is there an actual grant that created the easement. If so, what it says could be important here.
From what I could find, or actually couldn't find, was that NY does not have any statutes controlling the issue. It is more than likely controlled by common law.
With that said, it is almost universally accepted the the users of the easement (dominant tenants) are liable for the costs to maintain an easement. In some states the actual maintenance is the responsibility of the dominant tenant, in others, the servient tenant (the owner of the land the easement crosses) and would bill the dominant tenant for the costs. That is for normal maintenance though.
In your situation, the servient tenants actually caused damage so, that is not covered under typical maintenance costs. If the servient tenant is basically refusing to do anything, your next step would be to consult a lawyer. Sometimes a scare letter from an attorney gets things moving. If it doesn't, you would be best served by having an attorney assist you in this. Be forewarned: it can be lengthy and expensive.
I am not an attorney and any advice is not to be construed as legal advice. You might even want to ignore my advice. Actually, there are plenty of real attorneys that you might want to ignore as well.