Operating system: Windows-10-10.0.18362 64 Bits
Graphics card: GeForce GTX 1080/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 431.70
Broken: version: 2.81 (sub 3), branch: master, commit date: 2019-08-26 09:27, hash: rB277875492564
Short description of error
I animate particle lifetime to control the flow of particles from an emitter (setting it to 1 to cut off the flow). Unfortunately even after baking particle dynamics rendering in Cycles will cause the whole system to cut off/die when the lifetime of the particles is animated to a value of 1. This doesn't happen in viewport or anywhere else; only during Cycles render.
Exact steps for others to reproduce the error
Make particle system that has initial velocity from face(s), using an object for render.
Use keyframes to animate the particle lifetime with "constant" interpolation. Set the lifetime to 1 when you want to cut off the "flow" of particles.
In viewport this will look as expected and the existing particles will continue to exist while new particles have a lifetime of 1.
Use Cycles render to render the animation: at the point that the animated value for lifetime is reached ALL particles emitted, old and new, are destroyed.