I have not experienced "DevTools closing every time I step away from my laptop". It remains open for days if I do not close it.
Although I think what happens is that you might be sending a lot of requests and the Developer Tools feature crashes due to perhaps an out of memory error.
Does it ever close when you are using your laptop?
Maybe the (unspecified) operating system has some logic to keep the memory usage down when the machine is idle and that causes an out of memory error (have not heard of such cases, though).