I`m pretty sure its a carb issue, not ignition. I`ll explain what its started doing..
Cold starting is fine, perfect in fact. I rarely have to use the choke & after a couple of minutes its comfortably & smoothly idling at 700rpm.
You drive for 10 minutes, turn off, go & do what your doing, come back & get in... starts instantaniously & usually runs fine.
Drive for another 20 minutes, stop, get out & leave it for 1/2 an hour.
Get back in, start (instantaniously again), BUT, it will not idle, you try to use the throttle to keep an even 7-800rpm, but even with the accelerator a few mm down, the idle is very erratic, like its flooding.
It`ll then cut out everytime you take your foot off the accelerator, even when changing gear, so you have to do alot of foot work when coming to a halt or when in traffic (splitting your right foot between the brake & accelerator). Its very distracting & makes people think your trying to race them or get their attention!
It still starts perfectly every time, but then dies constantly.
I`m pretty sure its using more petrol when it does it too.
I`ve turned the idle up a couple of times to compensate when it does it, it does stop it cutting out, but the idle is very erratic & it then runs on when you turn it off, again pointing to the solonoid.
The idle jet is the small one & I keep meaning to get a bigger one or take mine out a bit, but, its all perfectly clean & the fact its not a constant issue makes me think its the cut off solonoid.
I know you can chop the end off, but I dont want to do any bodges!
I`ve been trying to get on
ePER for over as week to see if its still available but as-PER usual, I cant get on!
I can't actually say that I've ever had one fail, except on the fuel saving versions with cutoff-control unit (those sometimes fail and then the fuel cutoff plunger tip gets cut off with pliers

A less-brutal solution is to wire it to the ignition coil positive terminal which I think is what your Uno has).
Take the top off the carburettor and remove the jets, blow everything out with compressed air - and refit the top without gasket sealant, as that tends to end up blocking the jets, don't ask how I know this

You know this anyway but I think an intermittently-blocked idle jet is rather more likely than an intermittent solenoid. Still, all things are possible. Clean the solenoid connections/solder any crimped connectors that you find?
Another likely possibility is an overheating ignition module (bad ground in distributor?) but that would be hard to get going again and wouldn't respond to a couple of accelerator pumps like a fuel cutoff-valve problem would.
-Alex