If I take the advanced combat training I mission and after a while I terminate it when login off, will it not show the next time I log in? I'm asking this because I don't see any more the beginner and intermediate combat missions any more in my PDA and they were a great source of combat and weapons skill points.

The beginner and intermediate missions are level capped, so once you hit level 3 combat, they are gone for good unless you start over. The advanced combat missions however, stay around forever and once you learn to splatter Assault bots and not go for Guardians they are quite simple to do too.

Also, don't confuse Combat TRAINING with Combat PRACTICE. The Training ones don't give rewards like the Practice do. The Training missions are repeatable, but only need to be done once, assuming you read the mission logs properly. The Practice missions are also repeatable, and should be taken anytime you plan of a little "free-form" botting.

I still take a practice mission when I go farm arklans (when I remember before getting to the arklan fields).

As far as my experience shows, the mission will not terminate on log off.

Some missions wont terminate on the log off,but most of them will.As far as i noticed,if misson wont terminate flat robotic voice in your PDA will say that.