It’s an old idea, that decedence is either a symptom or a cause of the collapse of civilizations- Rome, Babylon, etc. Has this idea been examined rigorously? While the Roman elite might have been extremely decedent, I doubt the vast majority of ordinary Latins had the leisure for such fun and games, or that tolerance of non-traditional sexual behavior extended much beyond the urbane. It would be like judging the mores of the United States as a whole by the inhabitants of Manhatten or San Francisco. Yet we’re constantly hearing warnings that <behavior you disapprove of> will lead to collapse and barbarism. Is this a valid socio-historical correlation?
I think you mean “decadent”. A “decedent” is dead person. 
I only mention it because it took me a moment to work out what you meant, and I wanted to save others from the same confusion.
The etymology of ‘decadence’ refers to the last decades of the Roman Empire. So there is certainly a correlation in at least one sense…
The first big problem would be to define decadence in any meaningful way. To a Spartan the Amish culture would be considered hideously decadent, what with no warriors much less any notion of wartime heroics or martial prowess. And to an Amish the Spartan civilisation with its tolerance of homosexuality and pantheism and extreme warlike tendencies would be extremely decadent. So who gets to decide on what constitutes decadence when two societies that we normally hold up as examples of austerity and privation consider each other to be mutually decadent?
When most people speak of decadence what they really mean is tolerance. Rome or Babylon were ‘decadent’ because they tolerated many behaviours that didn’t hurt other citizens directly. There may well be a tendency for tolerant civilisations to vanish because without rigidly enforced codes of conduct the society will fragment internally and become less effective at defending borders even if it doesn’t end in civil war.
But beyond that I can’t see any evidence that ‘decadent’ societies were any more or less prone to vanishing than any other.
You sure? from Vulgar Latin *dcadere, to decay.. Of ocurse Dictionary.com isn’t exactly the last word in etymology but that is where I had always assumed it originated.
I don’t believe that is the case. According to this site, which I’ve aways found to be trustworthy:
The things we associate with Roman “decadence” – e.g., lavish banquets and wild orgies – happened in the Empire’s early decades, when it was strong, and had long since gone out of fashion before the Empire went Christian, which was long before the barbarians invaded the West. It is really a mistake to blame the fall of the Western Empire on its “decadence.” And don’t forget there was also the Eastern (Byzantine) Empire, which survived for another thousand years as a Christian state, FWIW.
It may well be that in times of insecurity, people tend to percieve decadence more strongly: behavoir that seems inconsequental when times are good may seem wasteful and indulgent and unhealthy when things are risky. So an increased sense of decedence is a symptom, not a cause, of decay.
Also, when resources become scarce, memories of a time when resources were abundant may create a sense that the generation that preceded that scarcity was more indulgent and decadent, even if they were living in much the same style as the generations before them.