The answer is 13 days.
Assume that the animal is in the first cave and going clockwise, while the retainers start searching at the 14th cave and the 13th cave on the first day. Each day after that one retainer will keep checking the 14th cave and the other retainers will be going against the clock until he comes back around. If the animal would move anti clockwise, the retainer in the 14th cave will immediately catch it. In other scenarios the other retainer will eventually always reach the animal by closing the animal in.
The longest time the retainers would be spending to catch the animal is if the animal would hide in the first cave and stays there. This would mean that the retainer who is checking every other cave except for cave 14 will spend 13 days before finding the animal.