Cleaning a rubber tub mat

I have one of those rubber bathtub safety mats - the kind with the suction cups - and the bottom is always covered with black mold. I will probably buy a new one today, but how can I clean these? I've tried:
Bleach Peroxide Lysol Various Shower / Tub & Tile Cleaners Vinegar Commercial Disinfectants
but none of them remove the mold entirely, and it always comes back within the week. I've tried soaking and scrubbing, but it doesn't all come off. Does anyone have any advice?
Thanks, -Adam S.
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On 29 Jan 2007 06:12:44 -0800, snipped-for-privacy@comcast.net wrote:

Don't leave it in the tub after you shower. Pull it up and drape it on the side of your tub, suction cups up. The mold won't grow.
Nan
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I second that. The mold returns because, if left lying in the bottom of the shower, it never dries underneath. Lift yours up a few hours after a shower and it is probably still damp underneath. Letting it dry completely is the *only* way to keep the mold from coming back.
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On 29 Jan 2007 06:12:44 -0800, snipped-for-privacy@comcast.net wrote:

Bleach will kill the mold, but the mold will return. The mat MUST be removed from the tub and turned upside down after every use. A dry mat will not grow mold/mildew. There are mats that are mildew/mold resistant, but even these will need to be dried out after use. Be careful with rubber mats and where you put them--these contain sulphur compounds that can react with plastics, vinyl, and other materials.
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snipped-for-privacy@comcast.net wrote:

I have scrubbed mine using a toothbrush or kidney shaped floorbrush and a bleach solution to get under those suction cups, then VOWED to always hang it to dry.
I have a tension rod over the tub which is handy also for hanging any damp towels, drip dry clothing etc.
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