Many disability policies have a specific time limit on the duration benefits will be paid. Some pay to age 65 (or older) and others pay only for 1, 2 or 5 years. I do not know what you bought. In addition, many plans also have shorter limits on benefits for so called "nervous" and "Mental" disorders -- often 2 years.
Without knowing precisely what your insurance policy provides, and what the basis UNUM had for stopping the benefits, I could not speculate on an approach or your rights.
One key issue is whether or not you meet the definition of "disabled" under the policy - and some plans have an "own occupation" (in your case being an anesthesiologist) definition while others it is anything that a person with your functional capabilities and education is suited for, such as being a physician at a Doc in the Box, while others use a much lower test -- similar to Social Security Disability -- "able to perform any job that exists in the National Economy" which could be a gate guard or a cash register operator.
