Never had that problem on my Silverado. However, had the connector unattached on my Hummer's bracket, but it was due to smashing it on boulders a few times. There are a few companies that make the seven pin plug and actually will fit the GM wiring connector on the back side (harness from vehicle). Pollak is one mfgr.
The Pollak seven pin is inserted into the bracket and then 4 screws attach it to the bracket. Will need to do some drilling. As stated earlier, the vehicle's harness connector snaps into place.
I'll note that the Hummer's seven pin bracket is steel, and actually hangs a bit below the bumper, so with a Silverado or other GM vehicle, you might need to place a steel plate on the other side of the plastic bumper from the plug.
Just make sure to get the correct one for the correct year vehicle (if there is any difference).
Amazon.com: Pollak 11-893P 7-Way Sealed RV OEM Socket: Automotive