JD X595 Diesel mower no start after shuts down?

The fuel shutoff solenoid is more likely the problem, they can heat up and drop out, killing the engine or loose voltage to them and it will kill the engine. It is held by a relay, it has two coils in the solenoid, one to pull the solenoid and is a large coil, the second coil is a small coil which has to hold the solenoid. The best way to check is to wait till it acts up and then look to see if the solenoid is clicking each time the key is turned. The voltage drop could be caused by a battery not keeping up with the electrical load. The pto and the solenoid both require battery voltage and if voltage drops, you can loose the solenoid or the pto clutch.

QUESTION ?----

Is the solenoid failing of its own accord or is it because the battery is not supplying enough voltage?
And if it is failing through overheating, what could cause that? The tractor was definitely not running hot at the time.
The battery is the original that came with the tractor so now it is old. I guess, depending on how good it was to start with. I could remove it and take it somewhere for testing but it always seems to have plenty of power for the starter motor .
If the battery is OK can I remove the solenoid and take it somewhere for testing?

ANSWER:---

The solenoid can get hot electrically and shutoff THE ENGINE . But it can fail because the voltage drops. I would have the battery tested before I spent the money on a new SOLENOID.

--------------------

Another issue can be glow plugs.

The glow plug harness corroded at the relay and the main battery positive wire rotted right off the relay. No power to the brand new glowplugs. Or low power to glow plugs or the glow plugs not getting proper hot.

you can check the resistance on them too to make sure that things are good with the Glow plugs.

Start by pulling the plug and checking how hot it got then go back from there check the connections and wire then the relay or switch if the GP has its own button by the age i would really think to replace them since most newer ones get hotter faster.

----------

Also if PTO switch getting over heat then it will not let the engine to start , till it gets cool.