With 3 identical pitot tubes that have just experienced common mode plugging due to weather, you are going to have 3 identical steam generators that will attempt to keep the pitot tube interior at a pressure characteristic of the trapped water temperature. As long as there is water to flash to steam, the pressure in all 3 pitot systems should be relatively constant.
The problem is that it would require the average water temperature throughout the whole tubing to be identical.
Also the steam generators may be identical, but if the volume of the systems is signifcantly different the time to achieve equilibrium will be different between them.
With a long tubing in the stdby system it should take considerablư longer to achieve the same average temperature and thus steam pressure as in the systems with less volume.
Regarding flash boilers:
The constant pressure is achieved by the moving of the catapult in combination with a constant evaporation rate. If the piston wouldn't move, the pressure should rise.
I wouldn't rule out this theory though we may have to think further on how this could potentially happen.