Repairing Cracked Tile Grout

I just found this great website. I am sure that you have heard of it before. Follow the link below to "This Old House". Good luck!

How to Caulk Around a Tub

http://www.thisoldhouse.com/toh/how-to/step/0,,20050103,00.html

They do make a plastic edging that replaces caulking. I bought mine at Ace Hardware. It is in a roll and designed for tubs, but it might solve your problem. You could also replace the grout with molding (wooden) or something that won't easily mold. Obviously getting wet it is not going to last indefinitely though. Keep the area as dry as possible, too. Here is an idea...how about concrete? Very thin line of it. I doubt it much molds.