How can I keep an entry gate operating during a power outage?
Basically, what you want is a UPS (Uninterruptible Power Supply); it's a combination surge protector and battery backup. These are usually spec'ed for computer systems (server rooms, uptime-critical workstations like for call centers, etc) but as long as you keep the actual unit inside some weatherproof area like a garage, it should be just fine for powering outdoor equipment like your gate. Be aware that U.S. 220V UPSes are hard to find; most 220-240V supplies are designed for use with ordinary European single-phase circuits, which run on double the voltage but half the amperage as U.S. 120V circuits. You want it to work with a two-phase U.S. circuit, which is double the voltage AND at least 15A. That will make most 220V UPSes cry uncle.

The UPSes that will do the job are going to cost a bit of money (this one from MultiStar is marginal for the amperage draw you'll need, and it's $535: MultiStar 3000VA 220-240V 60Hz UPS). You will have to ask yourself whether it's cheaper just to buy a gate system that has its own battery backup specially designed for the gate.