I did some debugging and recognized that there was some strange behaviour regarding the sessions. They were already expired just when they were created.
And then I recieved an email from the Magento team which states that there are several issues with the latest release of Magento 18.104.22.168 CE.
Looking at the last point in the list, I noticed that it is a bug in the core of the 22.214.171.124 update. So I followed the advice of the Magento team and refused the 126.96.36.199 update and installed 188.8.131.52 combined with the latest security patch SUPEE-8788 instead.
Now everything works as expected.
Several issues with our most recent Community Edition 1.9.3 release
have been reported. Some affect functionality critical to store
operations and we are working on a new release (Community Edition
184.108.40.206) that is tentatively scheduled for the end of next week. Magento is aware of the following issues:
- Search results return all store product
- Some integrations using Magento APIs no longer work
- Bundled product prices do not update
- Store-specific attribute labels disappear
- Auto generated passwords do not work for some customers
- Exceptions appear for stores with disabled breadcrumbs
- Free shipping sales rules are not calculated correctly
- PHP warnings occur with the session timestamp variable
We recommend that you wait to upgrade to Community Edition 1.9.3 and
instead apply the latest security patch, SUPEE-8788, which does not
have these issues.
If you have already upgraded, are experiencing issues, and cannot wait
for the new release, the Magento community has created a module that
resolves the issues outlined above. It can be found at
https://github.com/digitalpianism/bugfixes. Magento has not tested
this module. If you decide to use it, we recommend you remove the
community module and upgrade to Enterprise Edition 220.127.116.11 as soon as
it is available.