The problem isn't just watering, it's the combination of watering plus the ambient humidity in your kitchen that's killing your succulents. Twice a week is way too much, but what's really making things worse is that near a sink you've got constant humidity - the plants aren't transpiring fast enough to dry out, so the roots stay wet and that creates perfect conditions for rot. I had the same issue at my place: I put some small succulents on a kitchen shelf, and even without watering them much, they were getting mushy because the room itself was too humid.
The thing is, at this stage, if the leaves are already dropping and the stems are soft, you need to act fast. Get the plants out of the kitchen immediately and put them somewhere dry - ideally a windowsill in your living room or bedroom with lots of light but not humid. Stop watering them completely for a good while, even if it feels counterintuitive. Succulents store water in their tissues so they can go a long time without drinking.
If the rot's really taken hold, you can try saving them: take them out of their pots, let the roots air dry for a few days somewhere dry, then replant them in a really well-draining soil mix (cactus soil plus perlite for example). Once they're established, water very sparingly - like once every two or three weeks in summer, even less in winter. Watering is just when the soil is completely dry.