Thanks for your replies. It is possible that another plugin causes the deactivation, but unfortunately there are so many plugins installed, that its not possible for me to deactivate one after another and always wait one or two days to see what happens.
I now tried to disable automatic updates and see if the plugin stays activated.
The versions are all up to date (wordpress 3.8.1). The host is http://www.novatrend.ch/ - no idea if the performing is poor... I have also no possibility to check the log files (they are server sided, right?)
I keep you informed about the try with the disabled auto-update.