MM - I would be a little careful of using a parts cleaner - do nto want to shift any grot out of the cleaner into the carb, but if it is fresh and new - OK - as for cleaning other parts, cases etc - great.
Champion plugs failing from new - have had the same with NGK and ND - it is not unknown on any make I understand.
This problem is a cycling thing - runs Ok and then dies (sorry thinking out loud here) but when it is running you seem to be well made up with the bike - so we know it is a problem that can be cured - bike runs fine sometimes - and you want it cured - you like the bike when she is going.
It dies when it has been running for a bit - whether it is ticking over or being revved - suggesting carb picking up dirt - would cause the engine to run rough on the jet that is blocking or stop, but would not overly affect jetting away from this - ie if it is a blocking pilot jet, revving it up on to the needle or main would loose the problem. If the engine is just dying and not revving itself up then dying this suggests that it is not fuel starvation - the bike wil pick up revs and run quite well as the float bowl empties and the bike runs lean.
It is occurring when the engine warms up, this has got me leaning towards electrics now - but I would still give that carb another clean -
Please wait until others have confirmed this. Looking at the wiring diags on the following web site, your bike runs a CDI with spark info coming from the AC generator (alternator) so there must be the ign circ coil and a pulser coil or the like in there. The CDI is fed 12V DC through the B/W wire, the B wire is the earth and the O wire is the low tension to the coil. We can exclude a lot of the electrics from any test (this is the bit that needs confirmed before we cook your CDI) by chopping in a wire from the battery +ve to the B/W wire to the CDI - Thus if the vibration or what ever are causing the ign switch to cut out, kill switch etc, this will cut them out. Of course you will not be able to stop the engine once it has started unless you pull the wire from the +ve pole. - Personally I do not think the problem is in any of the switches - but I am often wrong. There are then three potential culprits. The CDI, the coil and the ign trigger in the alternator. I would start looking at the one one most liable to fail - the coil. Can you lay your hands on a CDI suited coil? Does not have to be the right one for the bike, so long as it is from a bike (car ones tend to be too big and hungery) - jury rig it to the CDI LT output a good solid earth and the plug. - You do not want to be touching it when it is up and running just in case. See if the engine will run up and if it does will it stop running again. If it is now fine - the issue is your coil, if it is not you may have two duff coils or the bike may not like the one you are using.
Jumping about a bit here... On the web site below it has the test resistance for the charging coil and the pulser coil, if you have a test meter you could check these when the bike is cold and again just after it has failed - there should be some difference between the two sets of readings - resistance changes with temp - but the magnitude of change should be pretty much the same for all elements - if not - if you get an open circuit, or even total resistance - this would / could be the issue. Ditto the same for the coil if you cannot lay your hands on an alternative.
Probably late to the ball but have been looking at this
http://www.slash5.net/sr500.htmlOh I would look to check resistances etc first - before I start poking wires in trying to short out the ignition switch etc - I mullered a Renault EMU by connecting up the wrong wire - right colour, wrong wire...
Hope some ideas help - kinda difficult being here in South Wales...