Any error in your sogod log? Any JavaScript error? Make sure to empty your browser's cache.

Cache has been empty, Java Script has been globally enabled.
When clicking on "save" just one line appears in sogo.log:
Jul 07 08:10:29 sogod [12483]: <client IP> "POST /SOGo/so/<client name>/Preferences/save HTTP/1.1" 503 46/6938 0.092 - - 44K

I noticed that the settings are saved despite the error message.

Do you use SIEVE?

No, SIEVE is not active.

What do you get when checking that user?
/usr/sbin/sogo-tool checkup <client name>

root@sogo:~# /usr/sbin/sogo-tool checkup <user1>
<0x0x1fc65d0[SOGoCache]> Cache cleanup interval set every 300.000000 seconds
<0x0x1fc65d0[SOGoCache]> Using host(s) '127.0.0.1' as server(s)
2017-07-11 10:46:18.653 sogo-tool[14651] Checking folders of user <user1>

root@sogo:~# /usr/sbin/sogo-tool checkup <user2>
<0x0x26b35d0[SOGoCache]> Cache cleanup interval set every 300.000000 seconds
<0x0x26b35d0[SOGoCache]> Using host(s) '127.0.0.1' as server(s)
2017-07-11 10:46:20.570 sogo-tool[14653] Checking folders of user <user2>
root@sogo:~#

Nothing useful, I think?

This means they do not have corrupt entries, which is a good thing.

Do you have the matching sope packages installed for your sogo version?

I tried it with a different not otherwise used browser (Chrome).
After clearing ALL browser data it works without error message.

After logout and login (with the same browser) the error message re-appeared -- until I deleted the browser data again.

Nothing in the logs, mysql error log is empty.

There are no user visable Java Script errors. Chrome runs "out of shelf", no script restrictions or ad blocker.

Has Christian wrote, can you share your installed SOGo/SOPE packages? Also, do any of the following parameters defined in sogo.conf?

SOGoSieveScriptsEnabled
SOGoForwardEnabled
SOGoVacationEnabled

Sorry, I thought I had attached a file containing required info.
Here it is:

libsope-appserver4.9/unknown,now 4.9.r1664.20170705 amd64 [installed,automatic]
libsope-core4.9/unknown,now 4.9.r1664.20170705 amd64 [installed,automatic]
libsope-gdl1-4.9/unknown,now 4.9.r1664.20170705 amd64 [installed,automatic]
libsope-ldap4.9/unknown,now 4.9.r1664.20170705 amd64 [installed,automatic]
libsope-mime4.9/unknown,now 4.9.r1664.20170705 amd64 [installed,automatic]
libsope-xml4.9/unknown,now 4.9.r1664.20170705 amd64 [installed,automatic]
sogo/unknown,now 3.2.10-1 amd64 [installed]
sogo-activesync/unknown,now 3.2.10-1 amd64 [installed]
sogo-common/now 2.2.9+git20141017-1 all [installed,local]
sogo-dbg/unknown,now 3.2.10-1 amd64 [installed]
sope4.9-dbg/unknown,now 4.9.r1664.20170705 amd64 [installed]
sope4.9-gdl1-mysql/unknown,now 4.9.r1664.20170705 amd64 [installed,automatic]
sope4.9-libxmlsaxdriver/unknown,now 4.9.r1664.20170705 amd64 [installed,automatic]
sope4.9-stxsaxdriver/unknown,now 4.9.r1664.20170705 amd64 [installed]

From sogo.conf:

SOGoSieveScriptsEnabled = NO;
SOGoVacationEnabled = YES;
SOGoForwardEnabled = NO;

If I understand the configuration manual correct SOGoVacationEnabled might be better "No" since at the moment we are not using Sieve?

Exactly.

O.k., thank you. It worked.

But I don't have to understand the connection between SOGoVacationEnabled and storing settings in the web interface?

When saving the preferences, sogod tried to update the Sieve script (because vacation auto-reply was enabled). Because it failed, it returned a 503 error code even if the other settings were save to the database.

Thank you for clarification.