If water is dripping through the downsatirs ceiling, it may be worse than they are just not drying off fast enough. Have you considered a leak in the pipe? Turn off all your taps and go out and check the water metre- if the numbers are still spinning with all the taps off, you have a leak. Is it a shower over a tub or just a cubicle with a tiled floor? In this case maybe one of those waterproofing companies can help (I've not used one so can't say if they are good or bad).
I guess no matter what it is it will cost you money at some point (hopefully not your life savings). good luck.
I guess no matter what it is it will cost you money at some point (hopefully not your life savings). good luck.