Newest posts get blank page!

I have a problem that’s already killing me:

Last posts (2-3 of them), the newest ones, are showing as blank pages. Other posts have no problem. Funny enough, as soon as there are newer posts, previously blank pages are shown as normal, but blank page problem moves on to haunt newer posts. However, the preview of posts is working fine as well, the problem is only when you click on the headline, or on “read more”, or in any other ways try to read the full post.

Other parts of website are ok.

Anyone knows what on earth is this? It started a few weeks ago, before that it was fine.

We’re always using the latest version of WordPress and all plugins are updated, we have even changed the theme hoping it will help, also tried to disable plugins, etc – NOTHING solves the problem.

Can anyone help? Website is https://www.app-kostenlos.de

A few more things: 1) other websites we have with similar theme, WP version and plugins are working fine even now.
2) Problem might have started after upgrade to 3.5.1 – if it’s not to blame, then it was just time coincidence.