Screen doesn't turn back on after resume on a Lenovo Thinkpad T420
As Dirk suggested, I'm adding the solution as an answer:
I might have found a fix for this by accident. I was reading about extending my battery life and it turned out the package "laptop-mode-tools" wasn't installed. The package doesn't work out-of-the-box on my notebook, but I found this: Unhandled kernel version error when trying to install laptop-mode-tools Since I installed this package, the problem seems to be gone.