First things first. Did you document when you first reported it, or was it just a telephone call?
Follow up with a written letter recapping what has happened up to this point (including what they did to "fix" it, bleach and paint). Then continue with the new developments (it's back x # of days later, and the wall is WET, etc). Explain that you believe there is some sort of leak in the wall that is creating it and ask them what they plan to do to repair it and the timeframe.
Keep copies for yourself. You can hand deliver it, if you want, and write down the name of the person you deliver it to on your copy (along with date and time).
Get out your lease agreement and review what it says regarding repairs/maintenance. If they aren't following it, follow up immediately with more written documentation.
Contact the agency a previous response mentioned and find out what they say is required, or what they can do to help you.
It is possible to get out of a lease if they do not keep the dwelling habitable, but you cannot just unilaterally move out or withhold rent. Go through an attorney if it comes down to that (hopefully it won't). I actually had to do something like that once. We ended up making our rent payment payable to both the apartment AND the attorney jointly, so that it was technically paid, but not cashable by them without making the necessary repairs.
Remember that all mold doesn't generate the toxic stuff. Not all molds that are black are "black mold". And it isn't the mold itself that is dangerous, but the mycotoxins that some molds produce. So don't go freak out on them. But if there is continuing moisture, it is in their best interest to find the source and correct it before structural damage occurs to THEIR property.
