We had a similar issue with our 2002 Sedona. It turned out to be the vent solenoid filter. It is located just in front of the gas tank on the drivers side of the vehicle. It snaps onto the rear side of the fuel vent canister. I manged to do it myself for about $25.00. I,m guessing a shop would charge $25.00 for the part plus 1 hour labor. It was not that difficult to change. Getting the old hoses off presented the worst problems. If you remove the filter, you should be able to blow through it with little restriction. The solenoid is normally open, so you should be able to blow through it as well.
Hope that helps,