I am curious about the solonoid. If it is damaged or not functioning would it still be able to shift to 4th like it so doing?
TL;DR: Yes. If the solenoid were restricted in some way (internal clog, weak coil only holding the valve partway open) it might not be allowing enough pressure to pass to hold 4th (OD) engaged.
The hydraulic control unit turns 3 inputs into fluid pressure (torque converter speed, road speed, accelerator position). These pressures work in the valve body, a complex series of passages, valves, orifices, and springs which balance these pressures against each other on a series of shift valves, determining which valves are open and which are shut, and therefore which gear is selected. It's a ludicrously complex mechanism, but can be broken down into smaller sub systems for easier understanding.
The 3rd/4th shift valve is the one we're interested in. It has flywheel speed pressure on one side trying to shift it to 3rd, and road speed pressure on the other side trying to shift it to 4th. Imagine you're in 3rd and accelerating. As road speed increases the pressure eventually overcomes the torque converter speed pressure and the valve gets pushed to the 4th position, shifting the gearbox up into 4th. If road speed drops, torque converter speed pressure overcomes road speed pressure and the valve gets pushed back to 3rd. Easy.
To complicate things, Mitsubishi added a solenoid to disable 4th gear. If the solenoid is off ("OD off" light on the dash illuminated), torque converter speed pressure is blocked from acting on the valve and road speed pressure will keep it in 3rd, even at high torque converter speeds or low road speeds. With the solenoid on, torque converter speed pressure is restored and can shift the valve to 4th. If the solenoid was clogged or weak, it might be partially blocking torque converter speed pressure from fully acting on the valve, and road speed pressure might be strong enough to shift it to 3rd when it shouldn't.
That's what your symptoms sound like to me, since it's shifting normally in other gears and doesn't seem abnormally slow. The solenoid is also well known for causing problems, and it's easy and cheap (if you shop around) to replace.
It might also be a number of other things, as sk66 says. Clogged filter screen in the transmission would lower torque converter speed pressure (but that would usually affect the other gears), faulty governor (but that would also affect all the shift points too, not just OD), gunked up internal passages/sticky valves/weak spring in the hydraulic control unit (that would *suuuuck*, but would involve replacing the solenoid anyway so it's easier to start there). Faulty pressure pump (more suckage- expensive!).