I'm glad that they did a biopsy. Even though they did not find a cause of the infection, the types of cells that were present may indicate a different course of treatment, so your vet may want to consult the pathologist who read the biopsy in order to get some additional ideas.
Also, if they have not already been done, dental x-rays should definitely be done. The cause for the recurrent hole could be that there is a root tip that is still present and is causing the problem. it is not likely that this will be detected with regular x-rays, but will require dental x-rays. Not all clinics have the ability to do dental x-rays, but more and more of them do.
Closing the hole can be more complicated than just suturing it closed. Since there is not a lot of extra tissue in the mouth, sometimes one has to do more complicated surgical procedures such as gum flaps so there is not too much tension on the sutures.
I do think it is time to consider a referral to a specialist in veterinary dentistry. I am not very familiar with New York or how far away some of these will be from you. Here is a list of specialists in New York. If any of these are a reasonable distance for you and you need more information about how to contact them, let me know and I will see what I can do.
Dr. Thoulton Surgeon - New Rochelle, NY
Dr. David Hansen - Cheektowaga, NY
Dr. Eric Davis - Fayetteville, NY
There are also two listed at Animal Medical Center iwhich is located at 510 East 62nd Street, New York, NY 10021 They are Dr. Dan Carmichael and Dr. Stephen Riback
Also, Cornell Vet School in New York very likely would also be a place that would have veterinary dental specialists.
Please let me know if you need additional information about how to contact any of these.
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