Not 5.1.1 -- this started in 5.0.
And according to the discussion at that bug report, not fixed in the current "M preview" (Android 6.0, in development).
The irony is -- 4.4, 5.0, and then 6.0 have all this new stuff to make battery use more efficient, with 6.0 actually going too far (severely limiting apps running in the background) -- and then we have this and other bugs which negate the effort and actually make battery use much, much worse.