Tested with a Sword and Short Bow, using Stone Spirit and Sun Spirit. rough average across about 20 tests is one proc every 15-20 successful hits, which is between 6.6% and 5.5%
Most of the time it seems to happen within the first 5 hits, then it will not happen again for another 15-20 hits. If there is some kind of internal cooldown, it is not indicated in either the tooltip or the spirit effect in the boon list. It’s also worth noting that the trait that increases the Spirit proc rate to 50% does not seem to effect the actual Proc rate.
Something is broken.