Can the BIOS chip be replaced?

Reputable. Okay, it looks like your board has a soldered on BIOS chip. Replacing it would be tricky at best, but possible if you knew what you were doing. You could go buy a new Z68 board.

Do BIOS chips fail?

Like any computer hardware component, BIOS (Basic Input Output System) chips can fail due to overheating, over voltage, or even the random interactions of cosmic rays making it down through the atmosphere. BIOS chips can be rewritten (or flashed) with updated drivers.