You can use it an infinite amount of times.
Protect's success rate decays by 50% each consecutive turn it, Detect, King's Shield, Spiky Shield, Quick Guard or Endure is used, with a minimum chance of 12.5%. This means a chart would go like this:
Turn 1: 100% Success Rate
Turn 2: 50%
Turn 3: 25%
Turn 4: 12.5%
Turn 5: 12.5%
Turn 6: 12.5%
Turn N: (1/2)^n-1 ≥ 12.5%
The chart that Immortal gave was for Generation III, as there was a glitch that made it not properly cap off at 12.5% and gave it a weird sequence of success rates.
This was fixed in Diamond & Pearl and Protect has worked properly ever since.