To my knowledge, no such list exists and there are no guarantees of a company big or small not being bought out in any given year. Its easier to spot companies which are likely to "fail" by looking at past performance (years established, management experience, and ability to raise capital)
It really depends on your perspective. Someone may see a host and think they are doing well and are going to be around for a long time, but then end up closing shop. While other companies people may have doubts about, but ending exceeding expectations... We don't know what is happening behind the scenes...
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Every host has a possibility to die out, so that is just poor Disaster Prevention.
Just back up your stuff regularly, and have a few providers on a backup list. Also ensure that they are compatible with each other, and the backup/restoration procedure is fairly seemless, or you'll be kicking yourself later on.
For example, cPanel/WHM allows you to create tarballs and extract accounts on the fly. It will make restoration a hell of a lot easier.
As everybody else is saying you should deffinitely look into the more established hosting providers.
Also look for hosts that arn't charging $20 dollars per month for 200GB storage and 1TB banwidth. These are also signs that the host may not be doing so well. If you really want quality, long lasting service spend the extra money.
As the others have suggested, no list would be available of who has staying power since you never know if a company will get an offer they can't pass on etc.. Or if they just don't want to put in all the time it takes to run a 24/7 operation. Jorge is right though, in saying that most of the older providers have a lot more longevity generally than the new kids on the block.
What I would suggest, is to look at the prices and features you are offered and say, does this seem like it's too good to be true, can the provider make money on my account, etc..?
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As stated previously in this thread, research any perspective companys and do a "whois" lookup to see how long they've truly been in business. I can't tell you the number of sites I've seen lately claiming to have been around for years with a newly registered domain.