It should hold it open, but if the solenoid isn't getting enough power to it, then you might find it fails to keep it open. Best bet with that is to feed 12v directly to both solenoids - if it drives as it should like that, then either you have a wiring fault, or the ecu is failing to provide enough power (Simon has said on a few occasions this can be worked around with using a seperate relay to control the solenoids, and using the ecu output to switch the relay).
It might be a useful diagnostic tool to put a 21w bulb in the place of the solenoid and see if it lights up properly or is dim, least then you know what you might be dealing with. Equally it wouldn't be a bad idea to check the battery pickup lead and fuse holder for corrosion or general grime, as I've found random problems can be down to a bad connection there. The fault you have is the same I had, I decided to swap the front end kit as it wasn't worth investing any further money into it at the time, as the car was reaching the end of its life at that point, and at least i could swap those bits to another vehicle then.
It won't work without the pressure sensor though.