This is actually an interesting issue because both the 1070ti and that i7 should be able to rip through even most intense of battles. And I've also met some... quirky performance here and there. For example, launching Icarus from a fresh start of Freespace sometimes gives me solid 120 FPS at the start when only looking at the skybox and then 70ish or more throughout the first scene, and sometimes it's under 90 at the skybox and all the time below 60 later on, and I'm not sure what exactly is causing this.
My suggestion for you is to take some monitoring software like the MSI Afterburner or something and monitor your RAM, VRAM and GPU usage with it and each individual CPU core with Task Manager. Maybe something becomes apparent.
In my case your own problem would make lots of sense - my GTX 770 tends to get its 2GB VRAM nearly topped off, so subsequent mission restarts could hamper GPU performance, but the 1070ti has got like... 4 times the VRAM I've got? That's really strange.