The EIS does a lot of things. It validates the lock/unlock signals from your remote keys. It reads information from the key when it's inserted and allows the steering column to unlock. It then receives a message from the steering lock motor and allows the key to be turned to the crank position. Then, it releases drive authorization data to the engine control module, which allows the starter and fuel pump to work. The fact that your issue is intermittent doesn't surprise me one bit.