My 1997 honda civic si is burning up it's EFI relay and we've replaced it twice.What could be the problem?

Exactly what were the signs that it was "burning up"?

We replaced the EFI relay and the car worked fine for about two hours,the we got another cheap EFI and replaced it again,the car worked for another couple hours

In all likelihood, there is nothing wrong with either main relay. Instead, focus on the ECM, which is probably intermittently failing. The main relay is controlled by the ECM, which grounds through Terminal 6 to the ECM. Perform the K-Test on the ECM:

The K-Test: Remove the MAP Sensor connector and turn the ignition switch to ON (Position II). Using a multimeter, check for 5 volts going between the MAP Sensor connector's reference wire (+) and ground. As you look at the connector, this is the socket on the right. Really press the black test lead into a cleaned main ECM ground on the thermostat housing. If the voltage is low, it's probably indicating ECM failure. Most failed ECMs will record a fraction of a volt. To me, the K-Test is simple, elegant, and accurate.

"The K-Test creates massive value, by providing a low cost solution where one did not previously exist."--TxGM

If you end up replacing the ECM, shop for price and warranty. Remove the old ECM, before buying a replacement, to ensure the new ECM is an exact Honda Part No. match.

We had the battery and computer unplugged all night and when we plugged everything back up she started.we went for a little ride in the car and when we got back she rived up a couple of times then I turned the car off and tried to restart it but no go

Perform the K-Test, when the engine won't start. It definitely sounds like the ECM is shot. Be sure to clean the ECM's main ground, located on the thermostat housing--you may get lucky.