You can release the terminal from the connector shell from the front and remove the wire from the rear. Push wire inward, tiny flat blade screw driver to lift locking tab, pull wire back and out. Fix contact retention friction as mentioned or crimp on new female contact...... but don't assume that is the problem until examination. You wouldn't notice one or two loose matings. "falls off easily" is highly unusual. It locks on. What have you done to that area lately? New or
donor switch, connector or contacts? Time to testify under oath. This is not our first rodeo.

Something funky in Denmark...or in your case, up in Bismarck.
Pics help a lot. Vendor and part numbers helps a lot. Ign Sw part number and pic is necessary. Showing male contacts. Show connector plugged on also.
Should be Packard 56 (Delphi 56) connector and contacts.
"typical connector with a plastic cover".......lets see that.