I believe you are not drying the area good enough, here is what you need to do,
Remove the old caulking and start from scratch. Here, dry all up, then you apply some rubbing alcohol to the area to be caulked to speed evaporation and to increase the ability of the caulking to adhere to the shower tile/base, etc.
I would also recommend that you use a hair dryer to speed the evaporation if moisture is present apply alcohol, let evaporate, dry area a bit with a hair dryer, let dry overnight, apply alcohol again and then let that evaporate before applying the caulk.
In my opinion, the very best caulk forTub/ showers is 1 HOUR SHOWER READY CAULK, open the link below, Good luck.
John
GE Silicone II* KB Supreme