Effect stops after 3:38, not matter what

Agents don't fix usage issues, they just make your software work if they can. Anyway, the answer is right there staring you in the face: Your effect stops because you are exhausting the Evolution parameter on the Fractal Noise effect. Modify the time variable with something like this:

(time%180)

so it resets every 180 seconds, i.e. every 3 minutes. If you want to have multiple layers to fade across, you can also simply subtract the in point:

time-thisLayer.inPoint

Mylenium

It makes sense when you know how effects values and/ or expressions in AE work and it also makes sense that it would even affect multiple layers when the underlying expression does not account for the in point and similar. So there you go. Select the layer, hit the UU or EE shortcuts to reveal modified properties and expressions, provide the code or screenshots.

Mylenium 

This happens when effects reach their maximum values, in your case likely driven by some time*x formula. You will need to reset the value in some form. If you provide the relevant code and info I'm sure we can work things out.

Mylenium