How can I improve the sensitivity of a motion detector light?
Removing the white plastic that covers the light sensor will make the PIR/motion sensor less sensitive/effective. The cover is actually a Fresnel lens, it has a pattern that scatters light in different directions, increasing sensitivity dramatically (e.g. when light passes through a part of the cover that is 0.5mm away from where it was before, it is sent into a different direction, making it appear as if it has moved more than it has).

I would suggest cleaning or replacing the cover (especially if it is old and has become damaged/dull/dirty). Some PIR sensors also have a dial to turn up or down sensitivity.

I know this is an old question, but it may help others.