Considering you can max your ranks in a month's time -- Its not going to last that long. There -is- a rank cap (300).
Where did you get that info from? Poeple on the Dulfy site say that even if you hit the caps as much as possible, it will take a year to get to 300. Not a month.
Seeing the weekly limit is less than what is needed to get a level for 2/3rds of the grind.... So 200 levels, with 1,5 weeks for each level is around 300 weeks.
I don't see how a month is possible. At least not unless you live on another planet.