Blazes will not shoot the player beyond 16 blocks. If the player runs the blaze will move in a perfectly straight path towards the player. In 1.7.10, the blazes have a range of about 40 blocks to shoot.
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http://minecraft.gamepedia.com/Blaze#History
The blaze's AI has been altered. Blazes will now attempt to attack the player even if there are blocks between them. A blaze will also alert other blazes in a staggering 50 block radius around itself of the player's presence upon being hit, causing all blazes within the wide radius to swarm the player, if they have a clear path. They now have a decreased firing distance: previously, blazes would shoot at the player from about 32 blocks away once angered, but they now shoot from only 16 blocks. When the player moves out of their radius, they will slowly "walk" over to the player, flying over obstructions in the way, but no longer pathfinding around walls and corners. When within melee range, the blaze will now actively rush towards the player and attempt to hit them out of melee range, and shoot fireballs once the player is out. They will not attempt to swim in water or lava, instead sinking to the bottom.
I wrote that on the wiki, by the way. I just wanted to see if it was intended behavior.

Well, lets see what the devs say.

Is that fixed in 1.11.2 ? MC-112013 claims so.

Confirmed to be fixed in 1.11.2
whay i can don't play minecraft
Create a new ticket, but search the tracker first.
Please close. Incorrect data. You are just unlucky with blaze shooting you. The blaze will shoot if it is max 20 blocks away from you according to my testing.