Prius park button works intermittently

You first need to fix your parking brake, it should hold the car without any issues.

You can simply shut down the car and skip the park button all together. But if you want it fixed, you can try another button or cleaning the wired connections

 

There is only ONE "Parking Brake" on a Prius and it is operated by your LEFT FOOT and is a Federally required safety feature which should be kept in excellent working order at all times.

The "Park Button" is the Prius equivalent of the "Park Pawl" or "Park Position" on a vehicle with an automatic transmission and they are not designed to hold the vehicle stationary (although most people do exactly that).

Based on your description, it sounds like the button (momentary switch inside) is not working correctly. That is, not making an electrical connection when depressed that would signal the parking solenoid to activate. There could also be a broken wire in the circuit or other damaged components like corroded terminals that are causing this.