I was also under the impression that the weather must improve x2 in order to make a 3rd approach?
FWIW I agree with the others here (e.g. Artie and Alex) in that there is no general rule. It will be down to the individual operator and will be stated in the carrier's Operations manual. For example our rule set ( and we are a JAROPS outfit) allows a third approach if the weather conditions are reported to have significantly improved.