The only time where we delete emails from our server is if a mail account is being deleted completely from our Mail Administration.
In case you experience that emails disappear from our server (from your webmail), the reason is often that you have a mail program connected where the mail program is set to delete emails after downloading them. This is the standard connection on the mail programs connecting through POP3.
There are several solutions to this. The first one is to re-configure the mail program to connect through IMAP instead of POP3. The second several is to reconfigure the mail program not to delete emails after they are downloaded from our mail server (Each mail program has such an option in their program).
In case you have any doubt as to which mail program that connects to your mail account, you can change the password on the mail account. After doing so, it will prevent the configured mail program from connecting successfully.