Debian is 32 years old. Arch is 24 years old. Gentoo is 23 years old. Alpine is 20 years old.

or do they often fail and vanish?

No. Niche, hipster, "latest hotness" distros sometimes vanish. Debian, Fedora, Gentoo, Kali, Qubes, Mint are all examples of community maintained distros that have been around for a long time.

Since you're looking for "stability" highly recommend Mint.

You've got that backwards. Community distros are more likely to be stable than corporate ones.

Pretty much all 'major' distributions (Debian, Ubuntu, Mint, Fedora, openSuse...) have 20+ years on their belt and none of those are not likely to go away any time soon. Some niche variants of those might vanish, but the main distributions will be there.

Slackware and Debian are the two oldest distros that exist (33 years). Debian is maintained by a group organized by a social contract.
Slackware is maintained by one dude in rural Minnessota.
Arch won't be going anywhere either.

You're missing the point of Linux. Generally, gnu/ Linux is a community based ecosystem across the board. Most of the software, most of the distros and most of the code you will use and encounter using any Linux distro will be community based. That's what gives Linux its advantage. The community can vet and improve any piece of code to improve the system for everybody.

You seem to have the false notion that corporate distros are safe (or something). But, that's not true. Look e.g. at the demise of Clear Linux OS.

For (perhaps) a better assessment on whether a distro is well-established^[I.e. that it will not cease existing overnight.] or not, consider looking at the following factors:

• How long does it exist? Like, if it's old enough to drink, then that's definitely a good indication.
• How strong is its community? If there are literally millions of users, many of which actively contribute, then that's definitely a good thing.
• How active is its development? The Linux landscape is constantly evolving. Hence, adopting changes (or, at least, enabling them) is somewhat to be expected.
• Does it serve a distinct raison d'être? It simply has to offer a strong justification for its existence.
• Does it have any strong dependencies/contingencies? Here, a lack thereof is actually what's good.

TL;DR: If you want to be absolutely safe, then I'd recommend Arch, Debian or Gentoo.

Debian, arch the closest are that u want

Any distro is stable as long as you don't screw something up.

The smaller/newer distros have no evidence of staying around for years, so it's hard to judge whether they'll be around in another couple years. Distros like Bazzite are definitely interesting, but you can't reliably predict whether it'll get updates in 10 years. There are stable community-led distros that have been around for a long time, like Debian.

Depends really. Small community distros serve a purpose as they either provide some niche configurations or pre-installed software that major distros don't, or they are made because they are trying to fork a major distros that is becoming too corporate with risk of becoming less open source. Now within community distros there are reputations. Debian is famously a community driven distro that hundreds of other distros are based on, and so is arch. They are pretty stable and will last more and more. Also, corporate distro doesn't guarantee longevity or stability either, because there are several corporate projects that get abandoned and are picked up by communities.

For cases where you just want to install it once and then update only once a month or even a couple months, and not worry about the distro not being maintained, I'd highly recommend installing Debian. You will eventually have to reinstall years down the line when a new major release happens, but it is many many years down the line and even that can be put off for quite a long time. The only drawback is that the latest releases of the software you like aren't always available in the official repos, as Debian's MO is to vet every package for stability before releasing it via their repos.

If you want a slightly less stable distro that has almost all the packages in the world and is up to date and is going to be around for a long time, go with Arch Linux. It's a rolling release model so packages are updated as soon as they are made available by the distribution maintainers. Things do break occassionally on Arch and a familiarity with the command line and where to go research/ask questions (the Arch Wiki and Arch Linux Forums) is very much needed in those situations. But Arch is very widely used and established nowadays and is a fine option if you're okay with the rare package that breaks.

Gentoo is a great option if you simply want to customize every aspect of your system, but it's considered an "advanced" distro and usually some familiarity with a different distro is recommended before using Gentoo, though some do end up using Gentoo as their first and only Linux distro. Gentoo, like Arch, is rolling release. Unlike Arch and Debian, packages are compiled from source, giving you granular control over which features of every piece of software you want to have and the ability to omit those features you don't want/need. Gentoo is as stable as you make it. Like Arch and Debian, Gentoo isn't going anywhere. That said, imho, Gentoo requires more maintenance than Arch or Debian, and potentially a little bit more knowledge of Operating Systems.

Other distributions like OpenSuse and Slackware are fine options as well as they have a very long established history in the Linux Distro ecosystem, but I am unfamiliar with them, so will leave it to others to make their comments/recommendations regarding them.

gentoo, slackware, debian etc all seem ultra stable