Small Engines (Lawn Mowers, etc.): John Deere LX188 stops after 30-45 minutes, john deere lx188, safety switches

Question
I have a John Deere LX188 that will run for aprox 30-40 minutes then acts as if it is out of gas and dies.  It will restart for aprox 3-5 seconds then dies again.  The next day the same scenario.  I have cleaned the gas tank, lines and carb.  Also replaced plugs (earlier) and fuel filter.
Since it will start at full choke for aprox 3-5 seconds I don’t know what to check.  Sometimes I can move between full choke and idle and keep it running longer than 5 seconds.
I know it sounds like it could be a fuel problem but if there is blockage why will it run so long at first?  Fuel pump??
This is a two cylinder and can actually run on one cylinder (poorly of course).  I believe it has two coils so if it is an ignition problem it would have to be something in common with both coils… right?  Could it be the ignitor??  I priced an ignitor @ $262.  
Any help would be appreciated.  Is there anything I should check before problem occurs or during problem?

Answer
Hello Jon:

There are Several Possible Causes Other than the Ignitor. 1- Check the Gas Tank Cap and Ensure it is Venting the Tank Properly. It Takes 30 to 45 Minutes, Depending on the Tank Size for a Vacuum to Occur in the Tank and Stop the Flow of Gas to the Carburetor. 2- The Carburetor Shut Off Solenoid Takes the Same Amount of time to Heat Up and Cause this Problem. 3- When the engine Quits; Does the Spark Plugs have Fire? If No, then Jumper Out ALL the Safety Switches and Start the Engine. If it Starts and Runs Properly for 5 Minutes, then Check the Safety Switches. Shut Off the Engine and Replace the Safety Switches One at a Time. Stopping and Starting the Engine After Each Switch is Replaced. If the Engine has No Spark After you Jumper the Switches, then the Igniter is Bad. You have to have the Jumpers Ready. You have to Jumper and Test as Many Switches as Possible before the Switches Cool. The Key Here is the Temperature of the Machine when the Problem Occurs. It is Rare for a Switch is Heat up and Stop the Engine, but it Does Occur. From your Description, it Sounds like the Gas Tank Cap, Carburetor Solenoid or the Ignitor. Again Check the Safety Switches Before Purchasing an Ignitor. It is Cost Effective. You can View a Breakdown/IPL of the Mower at this Site Addy, http://jdpc.deere.com/jdpc/servlet/com.deere.u90490.partscatalog.view.servlets.H... and Enter the Model Numbers and Click Find. Then Select the Sectional File. Then Select the Section of the Mower you Wish to View Online. Hope this Helps. I am here if you Require more Assistance. Let me know what Happens, Please. Thanks.

Good Luck

Respectfully

John