I know little about what is correct, but I have had a magnificent burrows tail for about 30 years and I neglect it terribly. I use regular potting soil. I put it outside each summer and give it a hair cut each fall when I bring it back in. If it is thin any where, I cut off a long piece, make a hole in the soil with a screw driver, and stick the stem in pushing dirt around it. Every 4 or 5 years or so, I cut it way back and replace some of the soil. It lives in a pot without drainage and gets a very big drink every two weeks. It's great! I never thought of trying to grow it in grit. Here is a picture. It did not get outside this summer due to a deck remodel so it is very long right now. If pieces that fall off, which they do all the time, I just drop them back on the top.

I have a hard time with these too. It comes down to not enough water for me. I'm gonna guess that's what's happening to yours. You gotta think all those leaves need good amounts of water to stay plump and to keep the stems full of leaves. Plus I've noticed they turn an ugly yellow when getting too much sun. So more water than you would think and filtered light I think would be ideal.

Luckily you can find these guys everywhere so if yours doesn't make it, they're easy to find;).

I find Sedum needs more water than other succulents in warmer zones, my burro's gets wrinkly leaves from being too dry if I water them about the same as my Echeverias, but plumps up as soon as I give it twice as much water as my other succulents.

@Frank and @Kara how often are you watering? It does sound like they need more water than I am giving them. I water about once a week.

I actually don't have any BT right now because they shrivel up and die or just look ugly, but I now know why mine never look good;). They just need more h2o. I think a good spot for them would be hanging in a tree. Watch out for squirrels. The light would be nice and filtered in a tree:).

I would say in a gritty mix and our climate twice a week, but it's starting to get cooler so you may be good with once a week. When it starts getting cooler protect them from those frosty nights. I find strings of pearls or string of whatever to be similar when it comes to lighting and watering needs:).

The one in your pic looks like you will have to turn into a cutting. The stem looks dead.

I water mine probably about once a week, but keep in mind, like Lynn in the first comment, I grew most of my Sedum in regular peaty mix, so my watering frequency is completely not applicable for you as you grow yours in gritty mix. Mine also stay outdoor on my balcony all year.

My sympathies, I've had an awful time with these. Mine do exactly what yours show in the photo. I do have one or two containers now that are getting nice size on them, after I moved them into mostly shade on a friends advice. I use rooting powder to root them in coarse sand, it still takes about 3 months or more. I have 2-3 types and have all the same issues with each. Sorry not much help. My suspicion is they like a warmer climate and plenty of water. I think it's hard fo me to give the right water because it's so cool here overall, which makes it easy to over water. Just a theory. But the successful rootings I had recently in coarse sand have been with no water, just left in the sand dry until the roots are really really full. That's because when I transplanted before with scant roots they'd just decline and die.

Grown in z5 - indoors during winter - in gritty mix. These are cuttings shown earlier, right now - all rooted within 2 weeks, no rooting powder, no fertilizer. Kept in direct sun from sunrise until about noon, dappled after that (trees in the way):

@lisasfbay so you are saying leaving them dry in sand the bottom of the stem did not start to dry out? I wonder what is going on there that sand without water would cause the plant to preserve itself, whereas gritty mix without water has the plant just shriveling up.

@rina I wonder if you have more humidity there?

Yeah, I don't understand it. My cuttings in sand would get moisture/splash, but never actual water.