Why does this Relay not oscillate
There are several possibilities as to why the relay does not oscillate:
  1) If the LED lit once, then the battery gets discharged after the first actuation and therefore can't repeat the activation.
  2) The relay contact IS oscillating, but you can't detect it (too high).
  3) The battery does not have sufficient voltage to "completely" break the circuit, but you "hear"the relay click once. 

To give you a more precise answer, I need to know the relay specs, the battery's power capability, and what is the LED doing (full brightness, dull, off)?