Created attachment 788278 [details]
backtraces of evolution

And nothing strange in Linux console

[mikhail@localhost ~]$ evolution
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin
DWPBase: /home/mikhail/.config/libreoffice/4/user/uno_packages/cache/uno_packages/luq0mqw6.tmp_/orfo4ooo-linux.oxt/base/../base/DWPBase.bin

(evolution:1955): evolution-mail-WARNING **: Failed to refresh folder 'm.gavrilov: Inbox': No response: Connection terminated unexpectedly
Created new window in existing browser session.

Thanks for a bug report. I see all background process idle, with evolution itself trying to get password for your EWS account, which doesn't seem to come. The evolution-source-registry process doesn't indicate any pending password prompt. It seems to be related to [1]. Trying to run /usr/libexec/evolution-source-registry from a terminal might show what happened to the password prompt. Let's move to [1] for further investigation.

[1] https://bugzilla.gnome.org/show_bug.cgi?id=680961

*** Bug 1000729 has been marked as a duplicate of this bug. ***

*** Bug 1009289 has been marked as a duplicate of this bug. ***

Created attachment 799312 [details]
evolution-source-registry debugging script

I see you get this often recently. Could you try to debug this by these steps, please? It is (as root):
a)   $ mv /usr/libexec/evolution-source-registry /usr/libexec/evolution-source-registry.orig
b) save the attached file to /usr/libexec
c)   $ chmod a+x /usr/libexec/evolution-source-registry
d) restart the machine

After the restart there will be created a /tmp/esr.log. It will be populated until you return back the original evolution-source-registry process, or update evolution-data-server (which will overwrite the replacement script). Consider adding also GCR_DEBUG=all into the script, at the beginning of the /usr/libexec/evolution-source-registry.orig ... line, to get more debugging, but I hope this will be enough for now.

Note the script only adds to the log, thus it can grow ad infinitum (disk size, folder quota and so on, whichever comes first).

The log can contain some private information too, thus I'd prefer not to attach it here, but rather send it directly to me. Please name this bug in message subject, thus I'll not overlook your message in my Spam folder.

Basically, when you get to the hang state, and the evolution's backtrace will contain string "e_source_registry_authenticate_sync" (quotes for clarity only), then you face this bug again and the /tmp/esr.log file will, hopefully, show some clue what was going wrong. You might keep the process running for some time, to not get the tail of the log cut (due to buffering), preferably kill it by:
   $ pkill evolution-source-registry -TERM
for which the process listens and closes itself gracefully. It's possible another instance will run immediately after you kill the currently running, thus do not be surprised of it.