Gomez, There are two common problems that will cause this, the first one you are aware of, and the solenoid is replaceable.
However before you do that, do a quick test with a voltmeter. Connect up to the starter solenoid lead and check what your voltage reading is when you engage the starter. If it's in the neigborhood of 9 volts or lower, no matter what you do to the starter you will continue to have this problem. The cause is a voltage drop from the key power through the various safety switches to the final destination, the starter solenoid. Over time, resistence tends to build up in the circuit and once the voltage drops to this value, you have a few choices. Go through the whole circuit and replace the safety switches, clean every connection, replace the starter switch and then maybe it'll work again for you, for a while. Or you can get a low voltage solenoid that you can wire in that will allow the low voltage you are receiving to actuate the solenoid and allow a full 12 volts to be applied to the starter solenoid. Now you can buy a solenoid from NAPA but I can't help you with a number for it. However if you have a JD or SCAG dealer nearby they have a kit available for this very problem that comes with a prewired harness, solenoid and instructions. I use these on the Kubotas (among other tractors) all the time.
The only problem is if you want the part number this weekend I can't help you. But if you can wait till monday I'll hook you up. I geuss there's a possibility that if you have either one of these dealers nearby they may know what I'm talking about.