E:D has graphics memory management issues. GPU Memory fills up quickly and performance starts to degrade once it's filled up, which is usually within a minute or two. With overall performance becoming unbearably slow (From 60-100+ fps on ultra down to 10-20 fps) because with a full memory, E:D fails to allocate more memory for new textures, which means that it first has to figure out what other textures it can unload, and this can cause stutter.
On a hunch, I tried something, and it seems to have fixed it. Now I want you to try and see if it fixes it for you.
Unplug your second (third etc) screen(s). Only leave the primary screen connected. Test performance, play for a while, and see if it now remains stable.
Yes, E:D is a very boring game that requires you to have youtube open on a second screen, and I'm not even talking about all the third party browser tools, so it's questionable how viable of a solution this may be for you. But try it anyways and report back if this works to prevent the performance degradation.