In a world without popping bubbles, your house would naturally gain a bit of market value every year. But this means that as the appraised value of your house rises, your property taxes go up as well. That is, unless you engineer a freeze.
Working with your local historical preservation office, main street revitalization group or historical society, you may be able to work out a freeze on property tax increases. Freezes commonly last in the neighborhood of 10 to 15 years, and they're usually based on plans to renovate your historical property or a promise to keep said property as-is without significantly altering its character.