I have an encore 2 (bay trail atom) I got Debian up and running on. With the stock 4.3 kernel, wifi works until the machine is suspended. Then the device disappears. When I check /sys/bus/sdio/devices, there are no devices anymore. I upgraded to kernel 4.4 to see if that would help, and now I don't see anything in /sys/bus/sdio/devices when I boot the machine, so it seems something changed between kernel revisions. I then tried compiling one and enabled everything I could find that said intel_soc and that didn't help either. I am not sure how to start debugging what the problem might be or how to go about fixing it. Any thought?

It looks like you'll need to make further changes on your Debian OS to successfully enable suspend-to-ram. This Debian link offers 2 solutions but they're both for the gnome desktop: https://wiki.debian.org/Suspend

Your 'suspend' issue is not so much to do with the linux kernel but the actual OS you're running (i.e Debian).IMO.
If there are continuing problems with suspend, you may consider installing Ubuntu or Linux Mint to see if it works better (since energy saving is important on tablets).

Also, you may consider installing linux OSs which are designed specifically for tablets (as opposed to full OSs for desktops - which will use up more RAM etc).