It happens every single match I try...

I don't snipe because just last night I had two chances to snipe someone in the side of the head and I missed twice before he noticed me. I did however manage to get the third shot off before he killed me. Oh yeah, I missed that one too.

1) Don't come back the way you left. When my enemy takes cover, I'm putting my crosshairs where their head will be. It stands to reason they will do the same. So, if I choose to pop back out, I try to do it with my head at a different level. That fraction of second they have to adjust up or down is sometimes all I need to win the fight.

2) Or just don't come back. In your situation, head up the stairs and hit him across while he waits for you (or move on to another target). I don't get the highest kill counts, but I like to remember that not giving points to the other team with my death matters a lot, too. So, change the angle of attack.