How old is the gas in the tank? Is it three years old? I have a trailer queen GT390 GT/CS which has been sitting for several years. Last year I introduced contaminated fuel into the tank which made a mess of things. Had to drain the tank, refresh the carb and it started right up and ran for about one minute. Sputtered and quit. I checked everything, very similar to what you described. I did not want to change the plugs. Finally I pulled and cleaned up the plugs (5 hours to do) and she fired right up and ran great. The next morning, it tried to start and coughed and sputtered and would not start. Decided to change the plugs, not just clean them up (another 5 hours down the drain) and she fired right up and has run great ever since. Long story short, you may have fouled plugs. Todays replacement plug for the GT390 is the Autolite 45. Tip: if you remove the valve covers, much easier to change plugs. (mine also had the smog tubes which is why it took so long).