you did not send a scene unfortunately, but most common reason - if you deactivate a modifier by question, you set it from independent to action controlled.
This means you have to activate it by action as well as a first step. So as a first question ( sequence is importand !) put a question for age is greater than 0 and drag your modifier to the activate slot. Then as a second question put your stopping criteria and deactivate your modifier again.
As an example, I start spawning and turbulence ( better seen than vorticity in this case) at frame 0, latter limited to group 1 ( only generating, not spawned particles) to make it more visible .
When generating particles have travelled a distance of more than 150, turbulence stops and they continue on last heading and when they are 60 frames old, they stop spawning ...