If I understand your question, the answer is zero times. With freshly watered plots when you plant the potatoes they will stay watered to full grown without watering them again.
I work on 12 hours between waterings. As potatoes take 11 1/2 hours to grow they don't need watering again after planting. You could get 2 crops of parsnips in (5 hours to grow) without watering the second crop at all. etc
If you plant potatoes in a fully watered plot it would be enough to bring the potatoes to full growth even without guano, anything less and it might dry out before it's fully grown.
If you put your potatoes away without running some fogger through their carburetors, you're never going to get them to turn over in the spring. Just a little tip. Unless you like kick-starting them.
Well, I tried going 12 hours without watering my potatoes other than the watering I gave them when I planted them. They didn't grow and the seedlings were dried up. They recovered when I watered them, but I lost some hours waiting for the full crop. I'll try watering every 6 hours and see if that works for me.
Perhaps you should file a bug report. I plant potatoes (ditto: cabbages) overnight, and the watering when I plant is sufficient to yield crops in the morning.
Some months back I did systematic testing of this. Things may have changed, but what I found was that plots stay wet for 12 hours, with or without crops growing in them. I specifically tested potatoes and found that one watering (immediately before or after planting) was enough to allow the potatoes to mature. If I waited more than 12 hours to harvest, the patch would go dry and I'd have to water to revive the plants, but at that point I would have mature potatoes ready for harvesting.
I tested this when I lived in Aranna. I suppose it's possible that crops gardens need to be watered more often in areas with dry climates.
Why must I then water them at least twice? Once I watered 3 times. My crops are always asking for "nourishment". Spinach may be the only crop that does not need more than the initial wet patch. The extra watering may be because I seldom play long enough at one time to realize a crop.
Yes the option is there to 'nourish' them shortly after you have watered. But unless they are wilted there is no need. Check the progress bar.
I plant potatoes regularly before leaving Ur for the day, about 9 or 10 pm in RL. They are still wet when I next log on in the morning, normally 8.30 to 9 am, not quite the 12 hours. But if I do have to have left them longer 12 hours seems to be when they wilt and the soil dries up, and changes colour
You can get an idea of how much time is left before a plot will go dry by looking at the blue bar. Crops will ask for water even though the plot is still wet and will continue to grow the crops. Once the plot goes dry, the growing progress of the crops will stop where it is and then will restart once the plot is watered again.
Plots must be fully wet before you can fertilize. So if you harvest a crop and then plant another in a plot that is still wet but not recently watered, you'll have to water before you can fertilize.
Watering doesn't cost much, and at highest skill levels at least, the rewards seem to be greater than the costs.
If you test carefully (i.e. water, make sure blue bar shows full, note time, check back just shortly before 12 hours have passed) and find your plots dry up before 12 hours have passed, I'd suggest putting in a bug report.