I'm reposting this from the Enpass Beta forum, as it doesn't quite fit in there any longer now that Enpass 6 is out of beta.
I'll be reposting tox1c90's report verbatim, as it still holds true:
He later updated it with the following information, after a few rounds of fixes from the Enpass folks:
And my own follow up:
I'd like to chime in to say that I'm still seeing this issue as well, in version 6.4.1, under the same circumstances as reported above (only occurs when minimized and running as systray-only).