Ask Mr. Smarty Plants

This is almost surely a moisture-related problem. Even in a rock garden, your Opuntia ellisiana (tigertongue) is probably being subjected to more watering than it can tolerate, and perhaps without sufficient drainage. You need to remember that these are desert plants, accustomed by millennia of experience to growing in fast-draining sand (when there was any rain water to drain) and surviving. They are succulents, holding moisture inside their structure, but moisture collecting around their bases or soil that is too moist will encourage fungus. To protect your other plants, you need first to remove the pad(s) that are appearing rotted and mushy; in fact, it might be necessary to remove the whole plant. This will help prevent the spreading of the fungus to other cacti near it.

You next need to address the amount of water that is being applied to the garden, either by rain or artificial irrigation.  You say you planted your rock garden three years ago; this may be the first time since it was planted that it has received very much rain. Since Central Texas is unexpectedly getting some rain this Fall and early Winter, it's possible that poor drainage is causing that water to collect. Under no circumstances should your Opuntia be receiving supplemental watering. At this point, if the drainage in your rock garden is insufficient to protect the roots of the cacti, there is not a lot you can do about it. If and when plants have to be removed because of the problem, you can replace the soil with a more sandy mixture specifically for the growth of cacti and other succulents before you re-plant. And don't fertilize. These are native plants that can get along just fine with the materials in the soil where they live. Fertilizing will only encourage fresh growth, which is going to be more prone to disease. 

From our Native Plant Image Gallery:

Opuntia ellisiana

Opuntia ellisiana

Opuntia ellisiana