The more you set minsup low, the more patterns you will get. And the number of patterns can increase exponentially when minsup is set lower. And when the number of patterns increase the algorithms get slower and consume more memory.
So if you set minsup too low, the algorithm will never terminate or run out of memory. And if you set minsup too high you will get no patterns or not enough.
Now, what is "too high" or "too low" depends on the dataset and the algorithm.
This picture from my PAKDD 2014 paper shows a comparison of the performance of the algorithm for the minsup values on the main datasets on the webpage:

Edited 1 time(s). Last edit at 04/15/2014 03:59AM by webmasterphilfv.