air just stops blowing and then it starts back?

This works best if you pretend you are talking to a mechanic, you need to give more details.

2009 kia rio, air condition stops blowing when on max.turn it off for a couple of minutes then turn back on, it will blow again.

you’re probably freezing the coils over. You’re not supposed to run it on max more than a few minutes when you start out to cool the car initially.

I believe shadow has the answer. I’d guess it is worse on days of high humidity. The coils can ice up.

Try running the AC in the normal mode and see what happens.