As mentioned in a previous message, a simple vapour lock could be the problem, its happened to other Leader/Arrow owners when out intially enjoying a ride out, there's a small venting hole/tube in the filler cap that when new would have had a ball bearing inside, shake the cap and you should hear it rattling around, sometimes they get stuck - the vent hole allows air to be draw into the fuel tank as the level goes down as the running engine uses it, if vent hole is blocked although engine will fire up and run after awhile it can stop fuel flowing down the pipe to the carb, a period of non use is usually enough for the air inside the tank to equalise so will allow petroil to flow to carb again, engine to start and certain amount of mileage to be covered before symptoms arise again and engine cuts out. Even with a clear vent hole on the Arrow its possible for the base of the seat to rest on top of the fuel filler cap and block the hole off, shouldnt be a problem on a Leader though resting on the lip of the bodyshell.
I would have been suspicious of a faulty condenser if you are running a standard points system (sorry if youve said you are on electronic ignition set up, missed it) - condensers can work perfectly when cold but break down when hot, and they get very hot fitted to side of primary chaincase however if a faulty condenser I'm sure you would have noticed a misfire of some kind.
If its not a blocked air vent and ruling out a faulty condenser breaking down then I would suspect the centre seal is faulty and breaking down, although your engine has been rebuilt, we dont know what seals were used, its not been confirmed but there is a suspicion of Ethanol in the petrol having a detrimental effect on some rubber seals, I've had to replace two centre seals this year on my Arrows, they were the single double lipped seal, on one engine the offside centre lip had gone completely hard although strangely the nearside centre lip was still flexible, this one gets the best flow of fuel circulating around inside, on the othe Arrow engine it started easily hot or cold and ran perfectly for a few miles before power dropped off and eventually began to struggle going up hills, opening the throttle made it worse although once top of hill had been achieved and back on flat road the speed would pick up and run as though nothing was wrong, did all the usual checks, ignition, carb, fuel flow etc eventually resigning myself to stripping the crank out to check the seals, found the double lipped centre seal in one piece and flexible but close examination under a magnifying glass showed that the rubber seals were subject of numerous fine cracks and presumably breaking down under load when engine was running. New seals had been fitted to this engine only a few hundred miles previously when crank was changed - what the two engines had in common was that they had been fitted using new old stock Ariel seals, obviously not a good idea now they are getting on in age and I now only fit newly purchased seals from my local bearing supplier and I dont fit Nitrile seals anymore but Viton Seals that are a reddish colour.
Also recently a friend who had fitted new crank seals to his Leader engine had a power loss within a few hundred miles, a strip down found the old stock Ariel centre seal had disintegrated, he too now fits Viton seals.
Hope the above helps, try checking the easy accessible things first but if problems persist you might have to remove the crank and change the centre and end cover seals.
In an early message you mentioned running the oil/petrol mix at 40 - 1 I reckon that is far too lean a mix even with modern 2 Stroke oils especially for old iron barrels fitted to the Leader engine, they need good lubrication would recommend at least a 25 - 1 mix.