I don't think it's a case of being desensitized, I think it's contextual.
Obviously, it is very sad when a member of our armed forces are killed in duty - that's a given. I feel deeply sorry for families and friends of all those killed.
However, we do not live in an age of consription (thankfully) and all of these lads (and lasses) have joined the army knowing what it's all about.
While the recruitment videos might show squaddies playing rugby and pissing around on the firing range, the reality is that you are joining to be a soldier. The job of a soldier is to fight, using deadly weapons, against the enemy, also wielding deadly weapons.
If you choose to be a soldier, you will be ordered into a position where you will be asked kill and may well be killed yourself.
Death is an occupational hazard if you are going to be a soldier, just like burned fingers is to a baker and tennis elbow to a typist.
It is not a nice business, but people actively choose this lifestyle with all its pros and cons.
So, ugly as it is, death is an unfortunate reality of active armed forces and is obviously not 'news' as much as, for instance, the untimely death of Gary Speed.