There are settings to prevent responses from reopening tickets. When we did this in our environment, for the exact same reason, the resulting behavior is that the ticket remained closed, and the response then just opened a new ticket. If you want to play with the settings (in 1.10 I will assume since you did not provide any environment information) they can be found at:Admin Panel > Manage > Lists > Ticket Statuses > Closed > Item Properties > Allow tickets on this status to be reopened by end users