On Mon, 26 Jan 2015 12:05:12 -0600, philo wrote:

I've had problems in the past and it seemed to do with me not removing
every last trace of the old stuff. A razor knife helped a lot.

I've seen recommendations to wash the area with diluted bleach, once
caulk is removed, allowed to dry ... supposed to help adhesion of new
caulk and reduce further chances of mildew or helping to prevent its
growth.