Thank youWelcome to the site.
When checking for issues you need to be able to replicate the problem when diagnosing. It could be a coil issue that happens when hot, it could be a fuel passage thing that happens when hot, none of the issues seems to happen when cold or sitting for a while. I would doulbe check the connection all arount the ignition and the spark again when it is actually giving you the issue. If it is not running and giving isse cold or not you will need to make sure everything is happening start with the basics, fuel, air, spark and compression and connections clean dry and making connection. Dianosing sporatic issues is a real PITA, good luck!
No . I'm thinking the fuel pump honestlyIntruders run on the battery and even even a slightly low charge can cause issues. You should have at least 13.2V at the battery with the key off. Carbs can start to clog up then somehow open back up then clog up again but will eventually stop working until cleaned. The fuel pumps are known to become intermittent before they go out.
So what would I do? The easy stuff first.
-Check to make sure your battery cables are clean and tight. Make sure to check the negative cable where it grounds to the frame. Use sand paper to clean each terminal.
-Add 3-4 ounces or SeaFoam to the tank and try to run it into the carbs. Do this for 3 tanks if you get it running.
-You can also pour the SeaFoam directly into the carbs and fill them up. Let it sit overnight then drain the float bowls and start it up. Don't waste what comes out of the bowls just strain it through a cloth and use it in the tank.
-Take the battery to an auto parts store and have them load test it.
-If you want to go for it you can test the fuel pump. There are instructions in the service manual. I will PM you a link to the manual.
-Do you have an inline fuel filter? The bike does not come with one but some people install