For what it's worth- my 2001 had the same issue on a couple of occasions. Both under cooler temperatures, but I doubt that was a contributor. Of bigger significance was the age (~14 years) and mileage (in excess of 350K) at the time it happened. If I just let my truck idle for an extra minute or so, full steering/brakes came back.
I wondered the same thing (check valve) and suspected that the PS pump may have been a contributor. When I finally sold her, the steering was getting noticeably stiffer but still tolerable. Good luck.
"Chessy56"
So. Milwaukee, WI
'01 2500HD, LB7, ~440K miles
"Stock" engine. Dual fuel filtration system with Kennedy lift pump, BF Goodrich Commercial T/A Traction tires (sold to a dude from Texas- it's living a warmer life just fine down there now!).
'17 2500HD, L5P (Happy Birthday/Merry Christmas to me!!!) Currently bone stock, 120K miles.
"Socialism is a philosophy of failure, the creed of ignorance and
the gospel of envy. Its inherent virtue is the equal sharing of misery."
Winston Churchill