It sounds as if the tub is moving due to poor support on the wall and causing the grout to crack along the edge of the tub. Two things to address here. You might want to take off the lower row of tile (if you can replace the pattern/color easily) and level the tub and repair the wall support. This is a big job and might be more than you'd consider now.
The other is that you're better off not using grout along the edge betwen the tile and the tub. If the tub moves the grout cracks - as you've seen. Use a good silicone sealant to fill the gap along the edge of the tub. Be sure to remove as much of the old grout as you can. I would recommend a marine grade silicone, since it will last longer. Or if you want to spenda few $$ more and do a lifetime repair - use 3M Urethane Marine Sealant. It's expensive but it seals and is flexible so it will not crack. It is made for sealing boat hulls beneath the water line, so it will last forever in a tub surround. I've used it and it does great job. Applies like any other silicone or caulk and since it moisture cures, if the tub edge is not completely dry it doesn't hurt the bond.