"To lose sleep" (no article) is a legitimate expression, but it seems to have two meanings:
Sleep deprivation due to loss of sleep time: I am losing sleep (missing sleep) and becoming more tired each day because of the amount of work we are doing on the project. I will have to catch up on my sleep once this is over.
Become sleepless, become wide-awake: If I go to bed thinking about the day's events I start to lose sleep. To become sleepless/wide-awake at midnight is really annoying.