Thought I’d post the answer to this in case anyone is experiencing this same problem in the future. You need to further adjust your settings in the “Layer Emitter” dropdown. Specifically you need to change “Layer Sampling” to “Particle Birth Time” and also change “Layer RGB Usage” to “RGB -XYZ Velocity”.
This will make the particles stay true to their life parameter when using the layer emitter in particular and prevent them from disappearing when sourcing a layer that is moving.
Hope this helps!