The age at which seniors stop paying property taxes varies by jurisdiction. Some places offer property tax relief programs for seniors, while others do not. In general, these programs usually have eligibility criteria based on income, age, and home ownership.
In most areas, for seniors to freeze property taxes or get relief, the property must be their primary residence.
In some areas, seniors will get a discount off of the assessed value of their property. For example, qualifying seniors may pay property taxes on the value of their property minus $25,000. In other areas, the property value might "freeze" at the value when the homeowner turns a certain age, say age 65. These policies are to try and allow homeowners to remain in their own during the period of time that their income may be fixed.
It is best to check with your local government or tax office for specific information on property tax relief for seniors in your area.