How soon does a flower replenish its pollen?

It depends on the plant and whether or not they have or need pollen. I found this interesting discussion. Just click on the link to read it.

https://www.helpfulgardener.com/forum/viewtopic.php?f=8&t=68220

Here's another interesting article to click on:

http://www.seeds.ca/pollination/pollen-and-flowers/pollen

The answer is .... vague. "So the amount of nectar present in the flower depends on how rapidly it is produced and how often it is removed by hummingbirds or bees. When most of the nectar is removed it takes a while for the supply to be replenished. " "Awhile" is probably not the answer you sought, but a few places I checked mentioned 24 hours, a week, a few days, etc. Sorry I cannot be more precise! http://naturerambling.blogspot.com/2014/08/how-do-flowers-make-nectar.html

I believe that nature provides so many pollinators, with bees being one of the most important and common, that it is unlikely your flowers will run out of pollen in your lifetime. Remember you also have all the other insects, such as moths and butterflies that help pollination occur. And although less common, the wind alone can be strong enough to blow the pollen from one flower to another.

A lot of people confuse nectar and pollen. These are two completely different products of a plant and are produced for different reasons. Insects do not "drink" pollen, they drink nectar. NECTAR is produced by some plants to attract pollinating animals (primarily insects). There is no set amount of nectar that is produced or replenished by flowers, it's tremendously variable. Many flowers produce NO nectar, because they don't depend on insects to pollinate them, the pollen blows from one plant to another in the wind. POLLEN is the plant equivilant of sperm - it combines with an ovule in the same or another flower to produce a seed. Pollinating insects help this process by transferring the pollen from one flower to another while they are drinking or gathering nectar, or eating and gathering pollen.

http://kids.britannica.com/students/assembly/view/53831

I don't think I have ever seen a flower form more pollen. Nectar, yes.