I've been kicked out of two servers today while having a leading score in both of them.
Been playing on the blue team, snatching Green's intel a few times per game - in both cases I've been kicked out of the server without any votekick (at least to my knowledge).

What's that all about? Envious admins?!
Started playing just today and already loosing interest, things like that take out all the fun out of the game.

The fact that the message says that it's either "you've been kicked" or "the server shut down" means it's possible the servers you were on were D/Ced from the master server.

They still appear on the server list (refreshed for a couple of minutes) and seem full.

My question is, can the server admin just kick someone?
And if yes, why not provide him with the option to write a message to the kicked user about the reason he was kicked?

Well, I'd say the only way to notify people if they're gonna get kicked is through in-game chat THEN kicking them.

Although I think the server host would need to first figure out your IP address then do something to refuse access to it.

It's not a ban, just a kick. I can go back to the server if it's not full. Resets the score for me, of course, but that's no biggie...
Last kick I got was when I was a few blocks away from the Blue base while carrying the Green's intel.

This game is still very unstable, you most likely just lost connection for some reason or another. I don't think it is even possible for server admins to kick players yet.

OK, that's what I wanted to know, cheers!

And you shouldn't care too much about your score, rather your teams score.