You need more advice, right??
Tile grout is probably the problem in my experience.
-- Did you use a grout saw to remove every possible problem area BEFORE re-grouting?
-- The soap dish is a frequent culprit. Saw and re-grout.
-- You must seal the new grout ... I apply three coats with drying time in between.
-- Daryl is exactly correct on his steps too.
Lastly, if the hole underneath does not let you see where the problem is, make it bigger. Drywall is no big deal but LEAKS are. If the drain itself is leaking (doubtful) you will need to access it from underneath to loosen the holding nut and re-apply plumber's putty.
Good luck and let us know what you did to fix it!