To be honest: I cannot see anything frustrating here. My understanding (!) is: When you use FindMinimum and it gives a result without any warning, then in any case the number of iterations was obviously sufficient - and increasing MaxIteration is pointless. If MaxIteration was too small then it throws a warning, displaying the (insufficient) number of iterations used. (Here this is provoked:)

But reading Daniels answer I get the suspicion that I might be wrong ...

I suspect it is usually 100 but might be different for some methods if they are considered to be more costly. Usually in similar situations I start raising to 200, 400, etc. Until either I get the impression it won't help (e.g. stalling in the same place), or I get better results.