I am wondering whether your string-of-beads has actually been over-watered. This could also explain the demise of your previous plant. As a succulent, it has organs for storing water within its leaves, enabling it to survive without water in periods of drought. Your plant will cope with being under-watered better than being overwatered.
When plants are over-watered, they can look very similar to under-watered plants. This is because over-watering damages the roots, so that plants do not have a good root system with which to take up water, and look as though they need more water.
I would suggest that you let the compost dry out and then water far less frequently. House plants need much less water in winter anyway as they tend to be growing less than in the summer. You may not see much improvement until this summer, as it will take time for the roots to regrow, but hopefully by then you'll have signs of new growth.
This plant does also attract some pests but you do not say that you've seen any signs of those.
I hope you'll be able to send us some good news about you string-of-beads next year.