Yes, there is a limit to the number of messages that can be sent to non-contacts.
Basic members cannot send any messages to non-contacts on XING.
Premium members can send up to 5 messages per calendar month* to non-contacts. They will be notified once this limit has been reached. This restriction is then lifted at the end of each calendar month.
If you reach your limit you have the option of sending a contact request to the person you wish to communicate with. Once the request has been confirmed you can then send that person as many messages as you wish.
(*for current premium memberships beginning prior to 20.06.2017: 20 messages per month, for current premium memberships beginning prior to 26.09.2012: 20 messages per day)