How can I prevent the iTerm2 hotkey window from losing focus?

(If anyone wants the answer as of October 2017)

For iTerm2 as of v3.1.3:

1. Open the iTerm Preferences window (Menu bar: iTerm2 > Preferences...) and select Profiles.
2. Select the Hotkey Window profile^* you want to change.
3. Click on the Keys tab inside the Hotkey Window profile.
4. Click on Configure Hotkey Window button, opening a pulldown dialog.
5. Check the Pin hotkey window (stays open on loss of keyboard focus) and Floating window options, then click OK to confirm.

You may need to close the Hotkey Window first if it's already open (or you can restart iTerm) in order for the changes to take effect.

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_{* Nb. Since v3.1 you can have multiple hotkey windows, so this is why I say "the profile you want to change", as there may be more than one Hotkey Window profile, unlike in the screenshot.}

Try this (for iTerm2 ~ v3.0.10):

1. Open iTerm2 Preferences > Keys Tab (not Profiles>Keys!)
2. Turn off option "Hotkey window hides when focus is lost"