When you start it, do you throw the choke back to run position? Also, are you pulling the throttle trigger after it starts (need to let it idle some --warm up--before pulling throttle).
If you did #1 correctly, and it dies after it starts running, you have a fuel delivery/clogged air filter problem, but it is probably the former.
How long does it run? How many pulls to get it to start? (many pulls could signal that the cylinder is shot--loss of compression). But to answer your question at face value, see below...
Possible causes:
1. Fuel lines hardened/tank seals bad, and you are loosing vacuum around fuel lines, where they enter the tank.
2. Partially clogged/bad fuel filter in tank.
3. Broken primer bulb, leaks--replace.\
4. Need carb service--hardened fuel pump diaphragms
David Pickwell, September 2009