Sounds like you might have a clogged vent line to the fuel tank. Remove the vent hose and try blowing thru it. Is your tank getting low on fuel? Possibly the reserve may not be working or a clogged tank filter. Next time it starts to quit try loosening the gas cap or pulling the vent line off the gas cap and see if it starts back up again.

 

Think you need to check the tank vent line for any kinks or blockage. Pulling the fuel cap just lets the tank get another slug of air so it can run for awhile.

 

Hi again .Just tried as as you suggested, no luck .this time I let it sit and idle for about 20 minutes and it did it.

 

When this happens check for spark. If it has spark then you can usually eliminate an electrical break down when it gets hot. Then I'd let it cool down and check rocker arm clearance. Possible as it warms up if the clearance is too tight to begin with,they can increase when warm causing compression to drop. If valve clearances are ok,then do a compression check when cold and one when it dies on you to see if it drops. May be the same thing happening if piston to cylinder clearance itself is the problem.

 

I think I am right in the only 05 KQ was the 700, and the cams work directly on the valves, so no rockers, a strip down to check clearances, and a major one to alter the shims under the bucket tappets. So I would advise checking compression before valves on a 700. Could be a coil fault, though I had one that burnt out the earth lead to the coil and it threw a fault code " failure to spark for 11 revolutions". Change the plug first, just in case. Most likely fault with any 450 to 750 KQ is fuel filters, the one in the injector isn't too bad to get at, this is moulded into the inlet, so a careful poke with a tiny screwdriver and a blow out with compressed air should fix it. The one in the fuel tank is a nightmare to change.