As a guy who does this sort of thing on buildings, I can tell you that a good rain storm helps you decide you have a leak, but not where it is coming from.

Use a hose. Start low, at either the front or the back, and move slowly up, covering both front and back. You will soon see the water inside, and can narrow down the cause fairly easily then! You have to lock someone inside to tell you when they detect water though.

Hope you have found the leak, but if not, use a systematic approach. Remember, air finds the easiest way in, water finds the most expensive.