The forum supports only a max of 100 messages, whether they be sent, received or saved.
In your general settings, it is possible to have an email sent to notify you that a PM has been sent to you. That email contains the message, so you can save the PM in your email account, saving the info, but keeping you PM's below the 100 message limit.
You can also set up the forums to send you a pop up message when you sign in that you have been sent a private message.