While it is hard to say for sure without having more specific information about your case, it would seem that what you are describing is sufficient to require additional concrete action on the part of your landlord. If he has refused your requests in writing, you could consider having your local Board or Health or Housing Inspectors come out and inspect your apartment (free of charge). If they find evidence of mice, they will cite your landlord and order him to fix it. You could also potentially hire an exterminator yourself and deduct the cost from your rent. There are a number of potential options available to you since the law in MA is weighted towards the rights of tenants. I would suggest you consult with an attorney who could advise you as to the pros and cons of each possible approach.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change.
In my opinion, if you are catching two mice a week, you have an infestation of mice. Under the sanitary code the landlord has an obligation to make sure the premises is free from rodent activity. Since you and your landlord disagree that this is an infestation, a visit from the local health department/inspectional services department should be the next step. After the health department documents the visit and assuming it finds an infestation (which means the recurrent presence of mice), your landlord will be ordered to exterminate them and should be required to document how it is done. Please be aware that you will have to take reasonable housekeeping advice. The health department should conduct a re-inspection. Request one if it does not.
You may have a claim for the interference of the peace and quiet enjoyment of the premises, or breach of the warranty of habitablity. The facts you provided, however, are not developed enough. You should probaby sit down with a lawyer to review the details of the situation including the notice you have given to your landlord.
My answer, above, was meant to help you understand some of the legal issues presented in your summary of the circumstances. It was meant to provide information only. It was not meant to provide you with legal advice or create an attorney client relationship. You should continue to research your situation and take the opportunity to meet with an attorney.