Intruders 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.I have a 97 Suzuki 800 Intruder in which I bought gas then my bike started backfiring sputtering and shut off I waited a few minutes it started back up and it did it again and then it wouldn't start i trailered it home thinking maybe I bought bad gas but I emptied the tank and it wasn't the gas I checked the voltage it's getting fire the fuel lines are fine i crank It Up the next day rode it around for about 10 minutes ran fine did the same thing and wouldn't start back up it keeps doing this what could it be?
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 them.