I recently replaced my neutral safety switch and my reverse lights worked. Then the following weekend when I took it out my wife noticed they did not work again. The reverse blinked but did not stay on while I was backing up. Any ideas why I'm having problems?

 

I'd doublecheck the switch on the shifter and its adjustment (if you have an adjustable switch - I'm not sure, I'm not an automatic guy). Because the switch is the only thing that controls your reverse lights.
The lights are powered from the turn signal fuse so if your turn signals work, the shifter switch should have power on it.
If you'd like to troubleshoot it with a test light, look for the blue wire and green wire (both thin).

Hope this helps.
Lou