I'm setting up "rigs" for animating, I set up a composition, for example of a hand at different angles that plays each for 1 frame. I then use that in my main comp and time remap it, allowing me to select an angle by simply typing in the specific frame. However, one of my rigs, a bird, is having some problems. It's 3 pictures, one with wings up, one with wings down (for flapping effect) and one that shows it dead (after hitting a window). I did an animation test with it flying towards a window, and used time remapping to change the frame from 0 to 1 and back every 5 frames. Sometimes, however, it decides not to work, and the bird just flies towards the window without flapping (the resize and position keyframes still work, oddly). I use the region of interest tool and the resolution/down sample tool to make it preview faster, and that seems to always mess it up. I even exported it once and the time remap keyframes would not work.
I think you should just animate the wing going up and down one time and use the pingpong loop expression. It will repeat over and over forever (unless you tell it otherwise) and you won't have to mess with keyframes.