If you look on the side of the Ppump (attached to the AFC), you can see the back side of the solenoid. If you tilt your head over, you can watch the plunger. There's actually two solenoids in one. There's one that gets power when you turn the key on and it only has enough power to hold the plunger up, then there's the big one that only goes when you bump the starter. That is the one that actually picks up the plunger. That way the big one is only energized during stating, and less current is used to keep it up during driving.
They get old, they get lazy. That's just something that happens. Larry B sells a bigger one that's not supposed to get as hot. I personally just took mine apart when I started having issues, I cleaned it, greased it, checked the bore, and hooked it back up. I've been trouble free ever since. I think mine started acting up around 260000 miles. I'm at ~290000 now. I've also been without a boot since my rebuild and I've had no rust issues since I greased it up before install.
Good luck!
EDIT: Be careful with touching it when the engine's warm. When they start dying, they eat more current and get kind of hot.