I had MATE installed in my Debian Jessie and it worked OK.
After some 'apt-get update' I discovered that I did not get MATE as my desktop but GNOME.
The MATE is also gone from the Session list.
How come that it just disappears with a blink of an eye ...

I doubt it. All 'apt-get update' does is refresh your list of available packages. It does not make any changes to your system.

If you can check your BASH history to see the actual commands you used, it would help us help you.

Probably what happened (based on my knowledge of Debian as a non-Debian user) is that you typed 'apt-get dist-upgrade' and when the computer gave a list like "100 packages will be upgraded, 30 packages removed, 40 new packages installed; proceed?" you typed "Yes" without actually reading the list. (You can recreate the actual chain of events using your /var/log/apt)

Jessie is Debian Testing and therefore you should expect many bugs and instabilities, and furthermore, I would suggest that you should be following the Debian mailing lists and reporting bugs as you discover them. To me this is the "social contract" of being a Testing user, presumably you are concerned with squashing these bugs to improve the experience for all Debian users?

Anyways, every single Debian Testing user I know got the "dist-upgrade wants to install the entire Gnome desktop environment" behavior. All of the Debian forums are abuzz with this right now. It is a very well-known issue (so there is no need for you to report the bug) and hopefully one of our resident Debian experts will be along to suggest a fix (other than *my* suggested fix, which would be to use Debian Stable).

You can find more info about Debian Testing here: http://www.debian.org/releases/testing/

Your guess was correct ... I used 'apt-get dist-upgrade' ... sorry that I didn't check that
Problem with stable version is that most of the applications are outdated ... pretty much useless.
I understand there are bugs in Testing but to swipe away MATE desktop just like that ... incredible

Debian stable is used on the international space station, so I wouldn't call it "useless!" But I understand what you are saying, good luck!

ps Please understand that part of Debain Testing is testing the upgrade process itself.

Odd.

I use Fluxbox on Debian and have run dist-upgrade from Lenny to Squeeze to Wheezy (I'm now running Sid) and my window manager and all its settings were never touched, and none of the non-default applications or settings I use were disturbed.

I didn't mean that Debian stable was useless - as a server product it is excellent ... we run it on all our servers.
But we don't run it on our desktop since the applications running on stable are not up-to-date ... and that is more or less useless that I can't have the latest version of a desktop software.
We have testing on our desktops.

also

It is a common misconception that Debian Stable somehow forbids or blocks the user from updating individual applications as necessary. (It does not; Debian is all about freedom, including the freedom to make your system as up-to-date as you like.) Furthermore it has been my experience that a dependable, well-maintained used car will get most drivers from point A to point B. The "useless" software in Debian Stable could, for example, be used to: fall in love on a dating website, write a pulitzer-winning novel, balance the books for your successful business, create a lovely piece of artwork, invent something that will benefit the human race, let your kids play educational games, etc. (and if you find these goals impossible to achieve using the provided apps, you have 100% freedom and the tools at your disposal to upgrade to a newer version from backports/testing/unstable/experimental, or install an app from outside the Debian repos).

But I understand exactly what you are trying to say, I don't mean to come off as argumentative. Just trying to help you understand some of the differences between Debian Stable and Debian Testing as I understand them, now that I have have been using long enough to watch it go through three development cycles. I personally don't use Debian anymore, because it doesn't fit my needs, so I certainly am not going to twist your arm that you should use it.

IIRC there were some dependancy issues with MATE and GNOME, it is possible that apt-get "updated" some of GNOME's dependencies, thus removing what MATE needs, because conflicts, thus removing MATE itself.
Are you sure that MATE was completely removed btw, try dpkg -l | grep -i mate to check for sure.

When I added 'deb http://repo.mate-desktop.org/debian jessie main' to my repository (according to Mate homepage) and made 'apt-get dist-upgrade' it works.