What sort of delay? Does the animation outright stop before starting again or does it just slow down?
If it's the former: is "interpolation" set to "linear"? In the action editor, try highlighting the first and last keys of your looping animation and go to "keys -> interpolation mode -> linear" or something like that. What this does is it removes the easing in and out between keys, and in certain cases makes the looping more seamless.
Also, does the delay exist when you play back the animation in blender (you can make it loop in the timeline), or is it only in-game?