I tried to solve this problem by removing the new web, then creating it again. That resulted in the fact that ISPConfig was creating Vhosts files with date appended so I copied the one without a date to a backup file and copied the newest file (with date appended) to Vhosts_ispconfig.conf. Then I tried to restart Apache manually, hoping to see some errors. Luckily I got just a single error, stating that the SSL certificate of one of my webs could not be found. I still don't understand how the certificate dissappeared, but I created a new one and now the problem is solved.