Seen on DST's blog:
I see two solutions, one social, one implemental.
Social would be something like a land rule: Please limit your water consumption to 1 water per hour. Or something like that. And I don't really see this happening in practice.
Other would be to have the resources at different locations regenerate at different times (e.g. 24 batches, 1-hour intervals, or 12 batches, I don't know what's reasonable, might even vary by resource), throughout the day. This way everyone has a window of opportunity in which to collect without depleting.
Possibility of simply having every pile regenerate gradually through the day is confounded by things like memory stones.