I've been trying to root three cuttings from my David Austin 'Heritage' rose. I've had the same experience as you on two of the three ... but the third one seems to be making it over the long haul. Either I just got lucky on that one, or there's success in numbers.

Randy

Are you keeping them in too-moist hothouse conditions for too long? As soon as mine have a few roots, they are moved out to dappled sunshine.

Cheers,
Michelle

Also make sure the mixture is moist, but not soggy. Soggy will induce the rot as well. And top-growth is not always indicative of roots. The cuttings have a certain amount of stored energy and they can produce some top growth even with no roots at all.

They are damping off. I spread milled sphagnum moss (not peat moss but finely ground sphagnum - the stuff used in hanging baskets) over the surface. it has an anti-fungus, anti-bacterial action. You can get it at your local garden center under the name of "No Damp Off." You don't need much, it is dust fine and very light. I also use it when starting seedings - great stuff.

Thanks for the help.
How does one "sterilize" the soil for the cuttings?
It's not too moist, I think (or at least it looks like it's not)

I use perlite and/or expanded Jiffy 7 peat pellets to start my cuttings. Neither require sterilizing.
The peat pellets nest in the perlite which holds them erect and provides a moist environment. Perlite drains well so the cuttings don't drown.
Misting nozzles on a timer set for 5 minutes every 2 hours keeps them amply moist.
For me, starting cuttings in peat pellets allows me to remove them from the perlite without damaging the tender new roots.
{{gwi:314999}}
I use the same perlite all summer. Although a few cuttings turn black, most remain green and take root.
I average 95% take.

Or just switch to coconut coir, and you won't have to worry about it. Best rooting medium I've ever tried.

where do you get coconut coir?

I get mine from a local hydoponics shop, but I think it's available all over. Even Spray N Grow sells it cheap now.