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I don't know how DAP compares to other brands, but peeling up right away suggests it's a problem with how the surface was prepared ahead of time vs the brand of caulk that was chosen. If the surface wasn't cleaned properly the new caulk can't adhere. You may find this helpful: http://www.ehow.com/how_1000545_recaulk-bathtub-tub.html
The other important point in that article was about using the caulk remover, etc to thoroughly clean the surface after pulling out the old caulk...if you had silicone caulk on there before and don't do that step, filling up the tub won't solve your problem.