The engine on my Red Max EB7000 bac...

Two things come to mind.
One, the tank cap is not allowing air into the fuel tank to replace the fuel that is going out. This results in a vacuum in the fuel tank until the pump can no longer **** fuel. Test this by running it with the cap loosened a little bit just to test it OR loosen the cap after it has stopped and see if it goes normally again.

If this doesn't do it, you have an air leak somewhere.
The common ones, in order of occurance, are as follows.

Between the carby and motor.

The crankshaft seal on the clutch side of the motor.
(clutch comes off with left hand thread)

The crankshaft seal under the flywheel, on the pull starter end.

I have had a spark plug leaking around it's gasket ring too, but that was a one of, and stumped everyone for a long time.
With the exception of the flywheel end, you can test with a can of starting fluid, spraying it into the areas mentioned until you get a change in behavior from the motor.
I the crank seals are gone, new seals will work for another period, but probably the bearings are getting loose and wearing the seals out.

The most common air leak problem on redmax or any 2 cycle engine will be found between the gasket between the cylinder and crank case. One person mentioned the blower runs fine for 15 minutes or so, then bogs down. Here is what is happening: the air leak from the cylinder gasket is causing a leaner gas to air mixture, thus causing the motor to run hotter. As the engine overheats, the aluminum piston expands against the chrome plated walls of the cylinder, causing the piston rings to get tight. Thus, more friction, in turn, causes the piston to not move as freely up and down in the chamber. If you keep running it like this you will damage the cylinder walls, the piston and the bearings. Remedy: The best thing to do at first sign of this problem is to purchase the cylinder gasket, the oil seals on the crank side and the fly wheel side, and the gasket kit that comes with the intake, muffler, and insulator gaskets. Replacing all of these gaskets at the first sign of bogging down after the motor heats up will extend the life of your blower. We have 18 of these blowers, and in every case where the crew leaders were complaining of the blower working fine for the first 15 minutes between job sites, this was the problem and the remedy.