At the beginning of your animation the particles get emitted as expected until suddenly they stop!

If you slow down the emit rate they stop later and when you increase the emit rate they stop sooner: you've hit the system limit. Every particle flow emitter has its own limit which you can set in the system management roll out.

To resolve this:

• kill of the particles when you no longer need them, use a delete operator incombination with a test (age, speed, collision etc)
• if that's not enough and you need more particles available at the same time you can increase the upper limit:

By default this limit is 100000, you can increase it to 10000000 (if your machine is fast enough!).

System limit may give the impression that this value applies to all particle systems in the scene, however as mentioned previously it's a setting per particle system.