Since my previous comment, I moved around the application bootup order on startup so that enpass is launched before firefox. By the looks of things, the problem seems to have mostly gone away (I've had it 2-3 times in 20 or so reboots).
I was hitting this issue intermittently on a Fedora 26 installation, but have since moved over to an Arch Linux installation where I am hitting it 100% on login. Weirdly enough, uninstalling the addon and reinstalling allows the connection between browser and Enpass to become functioning, and the process doesn't utilize any CPU. If I restart the window manager or reboot computer, same problem again.