What causes the third gear to pop back out to neutral?

This happens when the shift forks inside the transmission get worn out or the shift cables need replacement. This guide should help you understand what's going on and how to fix it:

https://www.2carpros.com/articles/why-automotive-manual-transmissions-pop-out-of-gear-and-how-to-fix

I would also check the bushings at the end of the shift cables to see if there is excessive play. Check out the images (below). Let us know what happens and please upload pictures or videos of the problem so we can see what's going on.