I don't know how likely- but is there maybe a wad of leaves not allowing the the clutch arm to engage?

Yup, sounds like leaves are jammed into the blade clutch. Turn the mower on the side and look at the blade clutch for debri. If all clean, the blade clutch may be worn and needs to be replaced. Sorry to say, replacement of this part cost $140.00 (part alone) However keep in mind, the JX75 is one of the best mowers out there and is no longer made. I own two of them and I have yet to find a better mower. The only mower I find close but not as good is the Lawn-boy commercial 22271 which retails for $975.00. I know, I own one and the JX75 is a better mower. Good luck with your mower.

Thanks for the response. I've got another JX75 that is not working and have been using for parts so I'll probably take it from that one. How difficult is it to change the blade clutch?

To be quite honest I replaced mine about fours years ago and don't remember the step x step way to go about it. The clutch is a one piece item and there is not much to replacing it. I removed the motor but don't recall if this was needed. Basically, you need to disconnect the clutch cable, blade, and drive belt. If your going to attempt it, go for it and I can look at mine and a lot more will come to me as how to go about it. I speak highly of the JX75 simply because I own two and recently went out to buy a new one or something comparable. I found out a few things. One, John Deere no longer makes any mowers and the ones they do sell are steel decks, I think their made by Toro. The $700.00 + Honda mower has 10 speeds, plastic deck and the drive handle/speed control area is made up of a lot of plastic. The Toro Commercial $1,000.00, looks nice but when I push down on the handle, as to lift the front wheels of the ground, it felt very heavy. Just this Friday night I bought a Lawnboy commercial model 22271 and it's pretty nice but not a JX75. It list for $975.00 and I got it for $675.00. Sorry to ramble here, my two JX75 are getting old, still work great but wanted a fresh mower and I was taken back as to what is out there. A lot of bells, plastic and whistles but no real quality. Basically, it comes down to any company can buy a motor, let's a Honda motor and put it on their decks but where it falls apart is the quality of the wheels and drive system.
Good luck with clutch and check ebay, they are on there from time to time.