What is your cow's udder like? Does she have large teats? My Twister does, and she never milked out very well on a machine, which caused her to get mastitis when she was at the dairy. (On the plus side, she is very easy to milk by hand!).
If the remaining milk was all in one quarter, it could be that the tip of the teat was folded under a bit inside the inflation. Sometimes this will block off the flow.
Make sure you stimulate the cow's udder well (cleaning her off and stripping out a bit of the milk) and then wait about 30-45 seconds before putting the machine on. This will help her to let down her milk.
If she's used to having a calf on her, you can gently push up on her udder with the back of your hand (the way a calf would with its nose) to help trigger letdown if she is resistant (I do this with heifers fairly often). As a last resort, a shot of Oxytocin will work, but cows can become addicted to it and refuse to let down their milk without the shot.
Massaging the udder during milking, and pulling down on the inflation if there is one or more quarters that still have milk after the others have been milked out, also may work.
And HEY! At least your cow doesn't try to lay down atop the milking bucket, like my Christine does!