It seems that, anytime I try to regulate the water flow (sprinklers) on some of my outside faucet, they slowly turn themselves off over time. I come back and the sprinkler is barely dribbling.
This happens with both the old faucets and the new ones that I've put in. I'm on a well but this is not a pressure problem. I am absolutely positive that it is in the valves themselves.
This does not happen if I open them fully, only with partial flow.
Has anyone ever had this problem?

I have, on both wells and on town water, and can't wait to see what the plumbers say!

Never heard of such. First question is has the position of the handle moved from the position you left it?

" I'm on a well but this is not a pressure problem." how do you know this? Does the pressure gauge show full pressure when the water has slowed?

You guys really have to be gardeners who leave hoses on low for hours. They have always gone down to a trickle and then stopped, well or not, and no matter what kind of spigot.

I know it's not a pressure problem because sprinklers on other faucets which are running at the same time (and also at low volume) don't change their output.

The valve handles do not change their positions.

joypulv - and we should just be satisfied with this ? I think manufacturers should have addressed this issue by now. Sounds like poor engineering.

So how long does it take for this to occur? Does it always happen to the same faucet? Does it always ways happen to the same sprinkler? Are the hoses between the faucet and the sprinklers the same. Are the hoses the same size? What happens if you open the faucet slightly after a sprinkler has stopped?

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I know it's not a pressure problem because sprinklers on other faucets which are running

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That is not necessarily correct logic.

I'd say that it takes about 3 hours or more. It has happened to me in every home I've owned that had a yard (4) starting in 1980 and right up through the present. I don't use sprinklers; just regular hoses at low volume, and soaker hoses. Regular spigots and no-freeze spigots. Single spigots and added on multipliers. They ALL slow down and eventually stop or almost stop.

And no friends, family, neighbors, or wily animals who might be following me from house to house, state to state, year after year, to turn them down or off. In fact, the handles haven't moved. When I turn them off, they take just as many turns to turn off.

hkstroud - the hoses are similar enough. It wouldn't matter anyway once you set the flows the system balances itself out. If hose difference caused this, it would occur almost immediately after starting the system, not 20 minutes later.
It does always happen on the same faucets.
I think that the mechanism (Gland-packing) that holds the stem from turning freely is insufficient on some valves. If there is not enough material no amount of tightening on the stem nut is going to hold the stem from turning.
If the valve is fully open, the flow is not restricted. If you close the valve down, it then is in the flow and I believe that small vibrations created by eddies in that flow cause the valve gate to change position.
Some of my existing valves (circa 1967) don't do this. I am guessing that it's because valves were made with closer manufacturing tolerances than they are today.
Also, you do have to turn the handles quite a bit to get flow going again, and thinking about it, the handles have to have moved because they are solidly connected to the stems.

My first thought is a loose washer in the hose bib (faucet). My suggestion is to turn off the water, remove the stem. Remove the bonnet nut and then unscrew the stem. Tighten the screw that holds the washer in place. If it were me I would just replace the washer at this time. Or you can just turn the existing washer over.

Joy,

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And no friends, family, neighbors, or wily animals who might be following me

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How about little green gremlins?

I just live with it, and accept OP's conclusion, and any others. I'm too old to care anymore. Gives me a reason to get off my butt and go check. And I do replace washers almost every year. As for gremlins, I have a surfeit of those. Why didn't I think of that?

Hkstroud- "That is not necessarily correct logic"

And the correct logic would be that the other faucets/sprinklers are magically overcoming the loss of pressure?