How often do miners prove they are storing?
Miners are constantly computing PoSts. They submit coalesced proofs once per proving period. A proving period is tenatively set at three days, but that is an arbitrarily selected number, and could go down to a day (or less) or even be a week (though probably not more).
See the storage mining cycle doc for more info: https://github.com/filecoin-project/specs/blob/master/mining.md#storage-mining-cycle