I am playing in 1280x1024 with Minecraft GUI Scale Large.
Never had a problem. Only in the Inventory Panel i can´t see the NEI items.

minecraft 1.7.10 EnderIO-1.7.10-2.3.0.422_beta EnderCore-1.7.10-0.2.0.31_beta
Forge 10.13.4.1558 CodeChickenCore-1.7.10-1.0.7.47 NotEnoughItems-1.7.10-1.0.5.120

I have try different versions and also, with only NEI and Enderio

GUI Scale Large:

Test with large GUI from RFTools:

With GUI Scale Normal everything is ok. But it´s too small for me.

I think NEI switches off if it has less than 3 columns of space left.

Yes. There is nothing we can do here.