The limit is 16 per hour. That is enough to find a patch of 3 diamond every 10 minutes in that hour. Is that not enough? The system takes the last 60 minutes into account; so say you found diamond at 0:00 (personal timer) then at 0:10, and finally at 0:40. You have exhausted your quota, but you can still mine more diamond in 20 minutes (from when you first found the diamond). Does this make sense at all?
The quota system has been improved, and upon next update we may change the limit to something like
8 in 20 minutes
20 in 60 minutes
50 in 6 hours
90 in 24 hours
With all of these being rules for diamond, quota being exceeded when any of these rules being met.
Of course these values aren't final, they've yet to be reviewed.