Have you got CS open on another device? I sometimes log onto my tablet and it repeatedly logs me out on my computer then. Also, it sounds stupid, but is the Pound open? I often get logged out whenever the Pound opens.
Maybe you should click the 'log me in automatically each visit'? Whenever you log in just make sure to tick the box and it won't log you out! Hope this helps!
probably your browser doesn't save cookies if just have it in one device, else problem is in your internet connection that disable/enable every time at once, ticking 'log me in automatically each visit' in login page should help
are you using VPN? VPNs change your ip when you enable them, then server thinks you've visited with different device, then logs out. sometimes that happen. as Echodino said