Your gas string trimmer must keep a balanced flow of fuel and air in the carburettor. This precise balance needs to stay consistent at all times. Whenever you reach an imbalance you will start noticing performance problems. When the trimmer bogs down after starting and then dies, this usually means either the gas or air flow has been completely cut.
Like a human runner, when the trimmer accelerates it needs more air to supply the oxygen to ignite the fuel inside the carburettor. If a runner, or your trimmer, lacks the proper oxygen it will slow down. If you stop the trimmer's air it will choke and die.
The air filter and air vents must maintain an open pathway to deliver fresh air in and expunge the dirty air out. You should clean your air filter after every couple of uses and check your muffler's spark arrester screen and exhaust port after every 20 to 30 operating hours. Keeping these holes open and free will help you rule out airflow as the reason your trimmer is bogging down.
Checking the Fuel Tank
Often when the trimmer starts but dies soon after the problem lies somewhere in the gas tank. The vent hole on the gas cap allows heated air inside the tank so it can maintain the proper pressure required to push gas up into the carburettor. A blocked fuel filter can also cause this loss of suction. Either dirt floating in the gas or dirt inside the filter's screen can cause the fuel to stop reaching the carburettor.
Fuel filters need replacing every season at a minimum or more frequently if you use your trimmer heavily. You also need to make sure the fuel filter and fuel line are sitting at the bottom of the tank, so even if the engine is tipped it will still get the proper gas. Also, make sure you are using only the mixed gas and two-cycle oil at the ratio stated in your trimmer's operator's manual.
Fuel lines, made of plastic, can break down quickly due to bad or old gas, which will also choke your carburettor. The main fuel line draws the fuel to the carburettor and the impulse line pushes extra fuel back into the tank. If either of these lines get obstructed your trimmer will bog down and die. You also need to make sure these fuel hoses maintain an airtight connection with the carburettor's valve.
When the carburettor gets a bit older you'll start experiencing problems with it. Usually the mix of air and gas is regulated in the carburettor's mixing chamber. So problems like a blocked jet or screen will cause these same bogging problems. A trimmer service mechanic will need to take apart your carburettor to determine the cause of your air and gas imbalance.