The keys should re-sync everytime you turn the ignition on.
If the engine light is flashing, it means there is a problem with the transponder in the key. Either it has been damaged, is not programmed, or is missing. Playing with the lock/unlock buttons will not resolve the problem.
The transponder on earlier Vx keys was separate - think it is part of the circuit board on the newer flip keys, but having never taken one apart I am not 100% sure.