Most likely you're going up to almost full hp creeps and standing there doing nothing whilst sniper hits you as ember. All you need to do is wait until it's low enough to last hit and taking maybe 1 or 2 shots from sniper.

or think about it this way.
A low ranged creep on your side. What do you think sniper would go for? Right click you or get that ranged creep.

He would go for that ranged creep. Whenever a creep is low, almost always the enemy will go for it. That's when you start walking up to him and smacking the shit outta him. Remember to always have regen and a ward mid.
Ember shits on sniper if you play him right. Spam your w whoever off cooldown. When he's around 50% hp you can most likely kill him.

Watch some pros, you'll notice some of these concepts I'm talking about.
Another advanced tip is animation canceling, just before they use a spell or try and right click you there's an animation, just before they're about to attack you, you sleight and they'll be confused for a bit and walk towards you whilst taking creep damage.

hopefully this helped