That's because the blinking is an individual movie clip embedded within the main root timeline...
It's a bit difficult to explain, but I'll give it a go...
You've got a thing called the root timeline, this starts at frame 1 of the animation and ends at (for example) frame 200.
You then have things called movie clips, these are little timelines all to themselves where you can animate things happening. Once they get to the end they start playing from the beginning again automatically.
Everything plays at the same frame rate, so if you put your movie clip into your root timeline they will both be playing.
So if I had a static picture of a head in the root timeline and put a 40 frame long movie clip of an eye with the last four frames as a blink graphic then every 40 frames the eye will blink, so in 200 frames the head would blink five times.
When you pause an animation the movie clips continue playing but the root timeline stops. If you pause Samuri Lapin animations in some places then he will continue running without actually moving anywhere