Cracked grouting above slightly moving bath

The grouting above the first row of tiles around my bath is cracked and at risk of letting in water. It's because the tiles sit on the edge of the bath, which flexes ever so slightly when you use it. I've made remedial repairs to the grouting every six months or so, working fresh grout into the cracks. But over time, the cracks reappear. What I'd like to know is, is it possible to fix the grouting more permanently? Does all the grout need to be chiselled out and fresh grout added from the plaster board? Or is there some kind of large, flexible bath border (at least 10cm high) that I can put over the top of that row of tiles to cover the cracked grouting and flexes with the bath? I guess what I'm trying to avoid is a costly complete retiling of the bathroom if possible! Thank you for your thoughts.