pb shifter won't go into reverse

Button pushes in, but won't stay engaged there when warm. Trans doesn't get into Reverse, either. All is fine when cold and first started up. Button goes in and revers goes in just like it is supposed to. Run it a mile or two down the road and reverse doesn't work anymore.

I'm not familiar with the pb linkage but if it is adjustable that sounds like it needs a little adjustment. I would first eliminate that the trans is the problem. Have the linkage where it can be easily disconnected after you drive the car to warm it up. Bring it back in jack the rear end up and set it on jack stands (so the car won't roll). Take the shift linkage lose from the trans and by hand shift the trans into reverse from park while the motor is running. It would be good to have someone sitting inside the car with there foot on the brake. If it shifts into reverse by hand then you know it's got to be the shift linkage adjustment.