Final answer:
The strong nuclear force prevents protons from repelling each other and maintains proton stability within the nucleus.
Step-by-step explanation:
The force that prevents protons from repelling each other and maintains proton stability is the strong nuclear force. The strong nuclear force acts between protons, between neutrons, and between protons and neutrons within the nucleus. It is much stronger than the electrostatic force that causes the repulsion between positively charged protons.