Designing Kitchens and Bathrooms - Caulking and Mold

Hello, thanks for any help you can offer, in advance.
When I moved into my condo, the caulking in between where the wall tile meets the bathtub was almost completely dissolved, and replaced by dark mold. Three times in the past 4 years I've scraped out the caulk, treated the area with bleach, and replaced the caulk with "mold preventing" caulk. Each time, within a couple months, the mold starts to grow back and takes over that area quickly. What can I do/use to get rid of the mold, re-caulk the area, and keep the mold from growing back?
Thank you!!

Recurring mold may indicate a damp condition behind the wall. Next time you dig out the caulk and do the bleach thing wait a few days before you put new caulk back in and while waiting have a box fan blowing on the walls to help dry it out. If the mold comes back again there may be a leak in the plumbing or in the grout up above where water is getting into the wallboard. If you have greenboard behind the tile you can bet on having to eventually rip it all out and rebuild the wall. Once that stuff goes bad there is no going back. Thats why it was removed from the building codes in January as an acceptable wall substrate in tub and shower wet areas.