I'd double check your wiring. There is no reason that it shouldn't work off of a battery if it works on a bench supply.
On thing in particular to check, is to see if the negative connection is solid from the motor through the relay to the battery. Many bench supplies have their negative terminal tied to earth ground. If you circuit has some connection to ground also, the negative connection might be getting completed by a different path. If so, then it wouldn't work from the battery that lacks an earth ground connection.