By default, no, Firefox should not be purging cookies until they expire or the user deletes them, but other software or plugins could be interfering with cookies in unexpected ways.
GTPlanet's "don't ask me again" cookie is set to expire ten years after you select the option. You can view it and all other cookies in Firefox by selecting "Tools" -> "Browser Tools" -> "Web Developer Tools". Click the "Storage" tab, then select https://www.gtplanet.net
under the "Cookies" menu. If you have selected "don't ask me again", you should see a cookie named xf_push_notice_dismiss
with a value of 1
and an expiration date roughly ten years from now.