For years, thousands of people in the rolling hills surrounding this city signed leases to permit natural-gas drilling on their property, thinking it was an easy way to earn a few hundred dollars a year.

Now, hundreds are suing to get out of those leases, contending the contracts' time limits have expired and are undervalued. But gas drilling companies are making a novel argument to keep the property owners locked in: New York's four-year-old ban on gas drilling using high-volume hydraulic fracturing is akin, legally, to an act of God or natural disaster that automatically extends the leases.