Hello Natascha,
Thank you for reaching out, and I am happy to help!
Can you please share more information about how the website stops working and what happens in the front end?
How did you determine that the W3 Total Cache is responsible for the issue you are having?
Can you please disable the settings one by one in Performance>general settings, save the settings and purge the cache after each setting is disabled, and see which one might be causing the issue?
Thanks!