This is only a guess, and could be very wide of the mark.

On Fast speed the timer counts down in three-minute segments. My guess is that if the game is paused at the end of one of the segments the timer doesn't move down, and nothing happens to the timer when the game is unpaused. If the game is again paused when the next segment is due, again nothing will happen. Only if the game is running normally will it count down. If you're in the habit of pausing the game frequently (to pick up mushrooms and collectibles, say) it is quite likely that the timer will fail to count down quite often, so extending the nursing period.

On other speeds the timer counts down in larger segments. Although the likelihood of the game being paused at that moment when it is due to count down is less, the time which is in effect added on is more.