The main reason why a low MAF might lead to a lack of power in statistic analysis is basically the number of samples required for you to get adequate observation.

For example, if the SNP has MAF of 0.001, then it means that you will need at least 1000 samples to observe it 1 time. And in order to calculate the association, you can imagine that you will need a reasonable amount of SNPs to be observed before you can perform association. So if you need 100 observation of the SNPs, then you will need 100,000 samples. Think you can also read this paper: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3480678/

MAF is the second most frequent allele

for example in rs202127474 MAF/Minor allele count: C=0.0002/1 minor allele is C with a frequency of 0.02% in 1000 genome 1 phase genome and was found in 1 out of 2500 people;

Ref: dbsnp