Sounds like you may have a short or bad connection to the locking solenoid.
I would make sure to have a good ground wire to the trailer that connects through the trailer lights connector.

Or your trailer is not getting the reverse signal.

If you have a chevy there is a separate fuse for reverse on the trailer. The fuse could be blown. Check to see if your reverse lights work on the trailer when in reverse. You can also reverse the flat plug and turn your headlights on to see if it work then.

It's the ground wire more times than not in this scenario. When in a bind you can tape a penny inside the actuator and back up if you don't have time to find the cause of the short.

Check the wiring harness close to the tongue of the trailer. In most cases, there is a white wire that will be directly attached to the frame of the trailer. If your trailer is older, it may rely directly on contact between the trailer and hitch. If so, then you can replace the older wiring plug with a newer one that has the ground wire built in. Then just physically attach it to the trailer.

I would still check and make sure that the solenoid wire has a good connection as well. t-tap connectors at times need to be reseated to make good connections as corrosion can set in over time.

Also could be the adapter if you have one. Just fixed one on a new ranger trailer and thats what it was ,it would work then it stopped working. Checked the wiring and stuff put my adapter on it and bingo. Solved the problem. Not saying that everyone else is wrong just something that it may be.