What might cause tickets to automatically solve or close upon creation?
Tickets can close via the specific trigger action Status > Is > Closed.
To find this information, open up the ticket in question and check its audit trail (see Viewing all events of a ticket). When you're viewing a ticket, you can find audit trail details by clicking the Conversation drop-down and selecting Events.
From there, determine which trigger fired on the ticket and updated its status. Once you have identified the trigger, you can look for the condition Status > Is > Closed.
The most common cause of this issue is follow-up tickets inheriting the ticket properties of the original ticket. Any business rule that closed the original ticket will also fire on the follow-up ticket for this reason. For information on handling this scenario see: How can I reset drop-down field values for follow-up tickets?
For more questions about Closed tickets, see the articles below.