If it fades out, it's not the solenoid. Solenoids are easy, either they are on or off (unless you're talking about an IACV, but I digress..) so that's not it. Maybe you have a blocked oil passage or something, like you're losing pressure after being engaged for a short time..
The only other thing I can think of is some other sensor is not working properly, and your ECU is changing something like timing or fuel..
Try a different O2 sensor maybe. Maybe your fuel pump or something can't keep up with demand, like your pump is dying or your filter is clogged. This really sounds like a fluid delivery problem or some sort..