This sounds like fuel starvation. This is usually caused by debris in the fuel float bowl or a dirty fuel filter (if used). Remove the fuel float bowl and clean out the debris. With the bowl removed use a spray paint can lid as a catch pan and check fuel flow. With the float down it should fill the spray paint can lid in about 10 seconds. If you do not have this much fuel flow you need to inspect the tank outlet port, fuel lines and filter (if used).
The 20029 & 20099 models came with either a Briggs & Stratton or Kohler Courage XT7 engine. I need to know what engine you have to provide any diagrams on what to check or clean. A n engine model number would be even better. (Please!) Since the post is labeled with the 20099 model I will cite that as a reference. This SERVICE manual should help you with repairs:
http://www.kohlerengines.com/onlinecatalog/pdf/tp2601_308.pdf
See page 27 of the manual for fuel filter location. (Optional if used) AN exploded view is on page 31.
If you have the primer bulb model see page 24 and note the ondition of the primer bulb and primer bulb hose. Any hole in the primer bulb or cracks in the primer bulb hose can also cause this symptom.
If you have the Briggs and Stratton engine (Model 20029) I need the engine number to get you the correct manual data please. Otherwise...this should help you resolve the problem.
Thanks for choosing FixYa,
Kelly