if you go into the medals tab, it'll have a date period on the bottom. in this case it says feb16 - feb29.
so that's how long it'll be before the medals disappear or get reset.
mine reset from the first one (event). but it seems like the medals seem to stay for 1 more event after the event you gather them in. I could be wrong, but that's what has happened so far.
but since it shows dates down there, I'd say that would be your best bet to follow.