A little leak, needs to be corrected

 

while u are there fixing your fuel leak pull your egr valve and clean it up

 

Im going to say you have bad ingnition module,The heat up engine dies.They cool off and they will start till they just completely die.Also With the rain you might have a crack in the dis cap.

 

Here is a site you should Bookmark for future ref. It is easyautodiagnostics.com and covers the 4.3L V6 with specific tests to perform....and good photo's, too. It lists the Ignition Control Module---ICM,both early and late models. Look for a post in this 2nd Gen. section by Blazing Chevy who's title said something like '2000 Blazer w/Vortec V6 runs rough when cold and then when warm smooths out'. His solution was the ICM was getting moisture in it making it run roough when cold, but went the engine warmed up the ICM, it dried out the Module and the engine ran smoothly when warm. The ICM is on the right of the ign. coil and attached to the coil and cost less than $50.00.