Why do bolt-action sniper rifles occasionally not kill in one hit?

Usually if you hit someone with a bolt-action sniper rifle, they die. But sometimes even when you hit them, they're only injured.

What causes a sniper rifle to only wound? Does it depend on where on their body the bullet impacts at (for example, the Locus from the Call of Duty wiki has the description: "Bolt-action sniper rifle. 1-hit kill to the chest and above.", which could very well mean leg-shots would get hit markers)?

Does whether you've fully aimed down the sights or not affect it?

It'd help to know the exact game, since they may not have the same numbers.

Basically you've already guessed right. A shot in the foot or leg does not always kill (well, usually it does not - only sometimes) granted the target has full life.

Let's run the math:

In most cases (not all!) a sniper rifle has a base damage of 70 points. Some can be lower when suppressed (50) or higher in certain cases (like 98 for some MW3 rifles). Aiming down the sight does not change the numbers.

The basic damage multipliers are usually 1.5 for the upper torso and up and Black Ops even grants a 2.0 multiplier for head shots (neck and up), so a direct hit there in BO is always a kill. The lower torso has a multiplier of 1.1 in most cases.

70 * 1.5 (waist and up) = 105 = kill
70 * 1.1 (legs, feet) = 77 = no kill

suppressed with no perk:
50 * 1.5 = 75 = no kill

Fun fact:
A shot in the finger is worth more than a shot in the butt.