You should have created a backup to restore it later on the phone or on the PC. If no backup was created for your chat history, even if the messages weren't delivered, then it's impossible to recover them. The messages are stored only for the active session. If you close, uninstall, delete the application, then messages are deleted. However, you can ask the developers because it could be possible they saved a session with the messages. Use the following emails to get in touch with them:
care@mxit.com
support.mxit.com