Stapeliads on the whole are robust plants that aren’t vulnerable to many problems. The two maladies to be on the watch for are root rot and mealybugs. When a plant falls ill, I find it often has both: plants stressed by mealies more easily succumb to root rot, and plants weakened by a run-in with root rot will attract mealybugs.
Root rot
THIS is what happens when you overwater (or in this case, over-rain) your stapeliad:
In my unprofessional opinion, there are two types of root rot that impact stapeliads: the base will go jelly or jerky. The example above went jelly and the plant will liquefy. The example in the ‘treat’ section below went jerky, where the stems can no longer receive water or nutrients so it will dry up and shrivel until dead. Either way the roots are dead and the plant is dying from the base up.
Prevent
Your culprits are wet and cold. First and foremost be sure to plant your stapeliad in an appropriate soil to avoid soggy dirt. Drainage is key! Ideally the pot should drain fairly immediately when watered. Use perlite liberally, or you can switch out the dirt for lava rock sand to reduce risk of root rot.
Stapeliads enjoy water regularly in the spring–summer growing season. Be careful not to overwater your stapeliads by allowing the soil to fully dry between waterings. Taper down watering in the fall season, then keep the plant dry over winter. A lot of stapeliads will survive freezing or near-freezing temperatures if the soil is kept dry. This holds true for a lot of ascepliads, including desert roses and plumeria. I quit watering when overnight temperatures start dropping below about 50°F (10°C), and keep my plants in a greenhouse to avoid frost.
It’s normal for stapeliads to discolor and shrivel some in their winter state. People recommend not watering at all over the winter, but I live in an especially dry climate and do give a light infrequent watering based on how the plants are doing. If they look fine, leave them be. If they seem to be suffering, give them water. Just don’t let them stay damp or get cold while the soil is wet. I pick warmer spells to water!
Inspect
This one can sneak up on you. The plant will seem fine one day, and the next day collapse. You want to keep an eye out for plants that are unexpectedly shriveling or have stems tipping over. Roots visible above ground may appear dry and dead. You may spot the stems going jelly early on if they have an odd translucent appearance.
Check your plants regularly for signs of ill health, but the bigger thing to keep an eye on is the soil. Don't water if it is still wet from the last watering. When you water, it shouldn't be taking more than 2–3 days for the soil to dry. If you find a pot has gotten drenched in the winter, immediately attempt rescue.
Treat
Thankfully most stapeliads readily grow from cutting so act ASAP to save what you can! If there is a large amount of salvageable plant, split it into several cuttings to improve your odds. Smaller, less mature stems have a lower chance of making it like with this huernia (Hell's Bells).
Cut away any diseased area, ensuring the cut shows completely healthy stem well away from diseased tissue. Use rubbing alcohol to keep your tools sterile between sections. I keep a spray bottle handy in the garden.
Okay from here I admit I don’t follow every step because these plants are happy to grow where I live. But this would be the golden standard of care:
Dipping the fresh-cut ends in horticultural sulfur can reduce the risk of root rot. If you wish to use rooting hormone also apply it while the cut is fresh. Allow the end to dry (this step is doubly important after root rot!) and callous before planting. When it’s time to pot it, you’ll have more success laying stems horizontally or at an angle in the dirt instead of poking them in the soil upright. Stapeliads try to root along their stems wherever they touch the ground, so new roots will come from the side of the stem. Poking them into the dirt risks the submerged portion rotting again. Don't water until the cutting starts developing roots.