Changes I make in customizer are not saved

Well... That wouldn't be my preferred choice. All the content is already there. WPML was the final stage. In fact it was ready to show the client for approval. Would it make sense to share the database file with you? Try fixing it? Starting all over again would be the last thing I like to do if you know what I mean.

When did the logo disappear? After activating WPML?

I'm not sure but I do think so. Could also have happened after switching from twentytwelve back to GeneratePress. I temporarily switched to twentytwenty because of the WPML error during activation.

What's the value of your theme_mods_generatepress option in the wp_options table in your database?

Hi Tom, it's 5

The value is "5"? Nothing else at all?

Yes, just 5. Nothing else.

Well, that's certainly strange. It should have your custom logo, navigation theme locations set in "Appearance > Menus" etc..

Can you delete it completely and then try to reset those things?

May be worth doing a database backup first just in case.

Yes, that did the trick! Website is functioning again. Thanks for your help :-)

Now the value of the table also looks very different:

a:15:{s:18:"custom_css_post_id";i:5;s:18:"font_body_category";s:10:"sans-serif";s:18:"font_body_variants";s:15:"300,regular,700";s:24:"font_navigation_category";s:10:"sans-serif";s:24:"font_navigation_variants";s:15:"300,regular,700";s:26:"font_widget_title_category";s:10:"sans-serif";s:26:"font_widget_title_variants";s:15:"300,regular,700";s:23:"font_heading_1_category";s:10:"sans-serif";s:23:"font_heading_1_variants";s:15:"300,regular,700";s:23:"font_heading_2_category";s:10:"sans-serif";s:23:"font_heading_2_variants";s:15:"300,regular,700";s:23:"font_heading_3_category";s:10:"sans-serif";s:23:"font_heading_3_variants";s:15:"300,regular,700";s:11:"custom_logo";i:2432;s:18:"nav_menu_locations";a:2:{s:7:"primary";i:4;s:8:"slideout";i:4;}}

It just happened again... And now I know exactly when and why. I changed the WPML language switcher settings from one menu location to another (from main navigation to top menu location). So I checked the database and yes, the theme_mods_generatepress value is now only "s". Nothing else. So I deleted this table again. And it was fixed again... Hopefully it won't happen when I change other WPML settings in the future but I will let you know.

WPML isn't functioning properly... I translated a page and when I visit it it doesn't exists. So I will contact WPML and let them know about my problems.

Glad you've narrowed it down - hopefully they're able to fix the issue :)