Using a battery charger instead of a battery?
After your edit to mention that it works correctly on a 9V battery, I expect the problem is that your 9v charger has some "smarts" and only charges when it "thinks" it sees a 9V battery attached. 

The charger could be checking a few things to see if it should start the charge cycle.


Existing voltage - the charger checks to see if there is a partially charged battery attached and only starts charging if there's some voltage coming in from the battery connector.  A "dead" battery isn't really zero volts (it would be 6 or 7V for a 9V battery.) 
Check for a load, and shut off if there's no load attached - the charger thinks there's no battery to be charged and shuts off.
Stop the charge cycle if the load is too low - it thinks the battery is charged.


Number 3 is the most likely, follow by number 2.



Thought of a number 4:

The charger is putting out pulsating DC and keeps resetting your circuit.  In this case, the capacitor that @JIm Dearden mentions would help.