I'm not 100% but I'm pretty sure it carries over no matter what as long as you make at least Bronze it keeps counting towards your months on the system. If you miss one month you're pretty much screwed tho unless you use medals to buy a day/month.

So like, you could be bronze for 14 months in a row, if you all of a sudden on the 15th month make Iron, it'll give you the medals for being 15 months of Iron.