Why does my grass die?

Quickly read though comments, did not see the suggestion to try different grass seeds.

 

Actually David I'd ...just for curiosity ...lay a couple of bits of hose and mark out the opposite corners in what ever shape you fancy to see how it might look...It would look rather good and and instead of making it look smaller it may well trick the eye into it looking bigger.

 

Just toss some clover seeds about.

 

Does that deciduous shrub on the left of your 2nd photograph cast a lot of shade in summer?
That could affect the amount of rain that gets into the grass.

 

If it is any consolation I have the same problem in exactly the same spot. Tried everything now I have planted grass seed in a large seed tray then I am going to dig it up put in some general compost then replant. Fingers crossed.