It does that when it has been left alone for too long. You need to dig and divide it every several years.

Shading could also be a factor. As a side note translation autumn joy is often used here but cultivar name is correctly 'Herbstfreude'. Same as with human names cultivar names do not change when the plant enters a country speaking a different language.

Sedums prefer lean soil - that is, soil that is not overly fertile - even sandy or rocky - no fertilizing and only enough water to keep them hydrated. Flopping often occurs when the plant is grown in enriched soil preferred by other perennial plantings or in less than full sun. It will also benefit from being pinched or cut back a couple of times earlier in the growing season. I've not found dividing to be necessary very often, in fact I can't recall the last time mine were divided. This is a plant that will benefit from tough love rather than too much attention :-)

Mine doesn't flop. The deer make sure that it never gets too tall! They teased me by just nibbling on it earlier in the year but as soon as it was close to flowering, it is eaten quite raggedly.

Cisco says to cut it back by half in May or June, I forget which. I also forgot to do it......