Can't save settings

Check your PHP logs for any errors and let me know what you find.

2016-02-15 20:03:13.951 [NOTICE] [2a03:c980::1:20:10:60525] [STDERR] ........ ............ WordPress .................... ............ Duplicate entry '2016-02-16' for key 'unique_date' .. .......... .... ............ INSERT INTO wp_statistics_visit (last_visit, last_counter, visit) VALUES ( '', '2016-02-16', 0), ...................... do_action_ref_array, call_user_func_array, wp_statistics_add_visit_event
2016-02-15 20:04:44.401 [NOTICE] [178.252.103.31:62152] Content len: 3406, Request line: 'POST /blog/wp-admin/admin.php?page=wps_settings_page HTTP/1.1'

Neither of those seem particularly enlightening.

Have you enabled the GeoIP code?

If so, if you disable it and try saving the settings what happens?

GeoIp is unchecked on wps_settings_page#notifications-settings
Empty geoip exclusions on wps_settings_page#exclusions-settings

On wps_settings_page#externals-settings page is no check near “Collect geoip data” but “Update geoip data” is checked.
(May be it’s different in english version, I have russian translation, so translate it now by my own)
“Update geoip data” the only check here.

Can you try disabling your other plugins to see if there is a conflict with one of them?

I use

Akismet
iThemes Security
Symple Shortcodes
WP Statistics
WP Super Cache

Okay, will try to it now again.
Disabling all plugins included stats and enabling only stats.
After that I try to add my ip to exclusions (#exclusions-settings), but after pressing save button nothing happens and after ~40sec timeout browser error.

That’s very strange, the only other thing I can think of that may be causing an issue is a PHP config issue, can you check your “post_max_size”, “max_input_vars” and “memory_limit” settings via php_info()?