Small Engines (Lawn Mowers, etc.): H5013 lawn tractor cuts off, tank lines, arinet

Question
My Honda H5013 (w/ gx390 engine) will run fine, sometimes for 10 minutes, sometimes an hour, sometimes a couple or more hours, then it just cuts off. Will do it whether in gear or not, mower deck engaged or not and at any throttle position. I have already done the following:
1) Checked/cleaned carb
2) Cleaned fuel tank/lines
3) Replaced spark plug
I have also unplugged the fuel solenoid below the gas tank and engine runs quite a while before sputtering and eventually cutting off (therefore, I ruled this out since it cuts off suddenly. I pulled the plug wire while it was running and it cut off the same as when I have the problem.
Does this sound like a coil? I can't find a parts catalog/service manual for it...Am I  on the right track?

Answer
Hello Frank:

Check the Gas Tank Cap and Ensure it is Venting Properly. If the Cap is Good, then the Coil/Ign Module is the Cause of this Problem. This is the 3rd or 4th Question About an H5013 Mower I have had. I Can Not Locate the H5013 Mower, but I have a Site Addy that Lists the Engine. You can View a Breakdown/IPL of the Mower/Engine at this Site Addy, http://hayward.arinet.com/scripts/EmpartISAPI.dll?MF&app=ASP&lang=EN&TF=Mainfram... and Select the Catalog American Honda. If you Hit a Snag or this Does Not Correct the Problem,  I am Here if You Require More Assistance. Hope this Helps. Let me Know What Happens, Please. May the All Mighty Bless You and Yours. Thanks.

Good Luck

Respectfully

John

PS: I am Allowed to Answer 10 Questions a Day. If you See I am Maxxed Out, then Try Submitting your Question at or Just After 8pm EST (US). My New Day Starts then. Thanks.

Respectfully

John