The seniors' exemption has upper limits on income - i.e., you don't get it if you earn too much - but so far as I know it doesn't have lower limits. If the town is saying that they're denying the exemption because of your parents' income, then it's possible that the county thinks your parents aren't reporting all of their income. The fact that the property was partly used for commercial purposes might have a bearing on the amount of the exemption, but since you didn't say that the notice said anything about that it's probably not the main cause for denying the exemption.
I would suggest that you check with a competent local tax professional who has experience grieving local property taxes. He or she should be able to give you a solid answer you can rely on (never count on answers you get online for free) and may be able to help your parents re-apply for the exemption and prove to the town that they're in fact entitled to the exemption.
My answer does not constitute legal advice and may not be relied upon by anyone for any purpose and does not constitute an attorney/client relationship or an offer to form such a relationship. This disclaimer is intended to be fully compliant with the requirements of Treasury Department Circular 230 and the terms thereof are fully incorporated by reference. If you wish to consult with me please contact me at dana@nytaxcounsel or visit my website at www.nytaxcounsel.com
The exemption is awarded on an annual basis. In order to sue the Town, your mother needs to apply this year, and if denied, she has the right to an administrative appeal, and then to go to court. It sounds like she qualifies.
If you'd like to discuss, please feel free to call. Jeff Gold Gold, Benes, LLP 1854 Bellmore Ave Bellmore, NY 11710 Telephone -516.512.6333 Email - Jgold@goldbenes.com