replace Leviton outlet
You are generally not allowed to use backstabs with 12 gauge wire.   If solid wire is falling off the screw terminals, tighten the screw a lot harder.  

If stranded wire is falling off the screw terminals, a lot of people have trouble with that.  There are techniques which help, like twisting the strands as you shape them, and making sure you are hooking in the clockwise direction.  But here's another option.

This link here mostly compares screw terminals to backstabs.   However, it mentions a third type, which they call "screw and clamp", and UL calls a "screw actuated clamp".  That's the one.

Instead of a backstab, it provides a hole (often, 2 holes) almost immediately behind the screw.  You loosen the screw, stick the wire in the hole and turn down the screw tight. The screw is threaded into a clamling plate, which squeezes down on the wire, clamping it firmly.  Check the listing on each outlet but generally they are OK for stranded wire.  

Last time I priced these outlets, they were in the $4 range rather than the 75 cent cheapies you can also get.  Of course they are a much higher quality outlet throughout.