Claus, I will type in caps so to clarify, NOT as I am yelling. You have a valid point that worked for you, But I think you only "put a band aid" on it as I think you will find you have a bad starter. ..Anyways here goes...
A agree... this is a bandaid solution that didn't address the root cause.
The solenoid is a copper coil wrapped around an insulating tubular form. An iron core, mounted to slide freely inside the core, is attracted to center itself within the copper coil when power is applied. One end of the solenoid core closes relay contacts to energized to the starter motor windings. The other end releases the fork so the pinion gear can advance into the ring gear for starting. Forces opposing this pull include friction and the return spring which retracts the core to the home position. Replacing that spring with one of lower spring rate, as Banshee suggested, will reduce the force required to pull the core home. This can leave more of the solenoid force available to overcome friction from worn parts or deteriorting lubrication. I think this is one of the more worthwhile suggestions explained here. I would consider this while the part is on the bench for cleaning and rebuilding.
This is a DC circuit, so it will follow ohms law for current draw. The strength with which the solenoid can pull the core to oppose the return spring, and overcome friction in the system is directly related to ampere-turns. That is the number of turns wound on the coil multiplied by the amperage flowing through.
The current flow is directly related to the available voltage and the resistance of the copper wire. Now, lets say the solenoid gets "heat soaked". For arguement's sake, lets say the solenoid went from room temperatures of 25C (77 F) up to 75C (167 F) , for a difference of 50 degrees C. Copper increases resistance by .39 percent per degree C. That means the resistance increased by 0.39 x 50, or somewhat under 20 percent. Current flow will drop the same 20 percent, meaning ampere-turns and therefore pull-in force drops by 20 percent as well.
If the solenoid can't operate with 20 percent less current flow, there is something wrong with the part or something wrong with the part's design. If it is pulling in, as evidenced by a loud click, then the contacts are burned up like Vikki explained. If the contacts were burned, they wouldn't likely work when everything is cool, but pitted burned contacts might act that way too. Just because a part is new or expensive does not mean that it's good.
If the solenoid isn't pulling in when it's hot or isn't capable of energizing the starter because it has burned up contacts, replacing it's relay function at a remote location will solve the problem a bad solenoid caused. You've just replaced a bad solenoid with a good one you mounted somewhere else.