I have had the same problem with mine as long as I've owned it and thought it had something to do with heat but now I believe it needs a little higher voltage to pull in when it's warm. If it will not come on after shutting it off when warm I'll open the hood and give the carburetor linkage a little push to momentarily speed up the engine and it will then energize the clutch.
I would not make any adjustments to the springs. Unplug the pto from the harness. There is a green wire and a black wire. Check for voltage there. If there is none, use a tester from the negative on the battery to the green, you should have voltage there. I ran a wire from the chassis to the black of the plug and mine fired right up, like it lost it's ground. Also the switch in seat should cause the engine to die if you turn the pto on without sitting in the seat. I am searching for an schematic for that model if anyone has one so as to find the cause, as my method doesn't sit well with me. I'm not sure what that relay is for, only had the mower this weekend. Darn nice mowers.
just tighten the clutch nuts one face at a time....my tractor did the same thing. my tractor pto works like new now ....i only tightened the nuts two faces. if you wanted to do this the right way with the same result...spend the money for the service manual and read about tighting the nuts two a sertin gap in thousands of an inch.
sence i didnt have the money for the shop manual...i did the poor mans fix....same result but less money.
trust me this works great!!!!!!
Your voltage regulator may be going bad. Check your voltage at the battery at first start up,
then again after a good warmup. It should stay steady around 14v. If it's dropping off after
warmup, the regulator is bad. Gapping the pto to all the same size is a good idea too, just make sure
they are all the same....can't remember the gap size at the moment.