Industry standards for tiled things says caulk at all changes of plane, so good luck with grout there. since it is against industry standards, I'm not going to suggest any kind of grout. Good luck. If the caulk is failing, it could be for several reasons...what is the tile attached to? Drywall gets used more than it should (NEVER) in a tiled shower/tub area. Also, the tub might not be level, causing water to pool against and edge, which will create problems, too.