Behavior remains unchanged through Mathematica version 11.1
As noted by kguler the Front End option:
MessageOptions -> "MaxMessageCount" does not appear to have any effect on the number of times a Message is repeated before
General::stop is issued and that particular Message is suppressed.
I would like to know if it is supposed to have this effect but is broken, or if it does something else entirely. I cannot find any documentation for this Option, and I cannot find any examples of its use either here or in the MathGroup archives.