I need to make some cookie to stay alive forever, because some website I use doesn't have "remember me" option when logging in.
Is there any plugin, or program for this?
https://addons.mozilla.org/en-US/firefox/addon/edit-cookies/
Instead of using auto form-completer, using this add-on made it possible to stay logged in to website forever
Your question doesn't seem like it must be about cookies - more that you would like the form details to be saved. If that is the case, you can use something like:
https://addons.mozilla.org/en-us/firefox/addon/saved-password-editor/ (although I use this tool, it does not save "quick login" style passwords but you'll have to try it).
General details about form management: http://support.mozilla.org/en-US/kb/password-manager-remember-delete-change-passwords
The idea behind setting an expiration date of a cookie is that your browser should automatically delete the cookie once the server won't accept it anymore.
While you can prevent your browser from deleting it automatically after some given time has passed, a correctly set up website won't accept the expired cookie and, once you visit it again, issue a command to delete it "manually".
Accepting expired cookies would be a huge security risk. Everybody that managed to sniff one of your cookies could use it indefinitely, without any way of stopping him.
I haven't tried any of them, but there are several addons for Firefox that purport to do this by periodically reloading a page in your browser. It looks like the only one that is compatible with modern Firefox versions is mSession Keeper https://addons.mozilla.org/en-US/firefox/addon/msession-keeper/.
There's also this highly rated addon for Chrome called "Staying Alive": https://chrome.google.com/webstore/detail/staying-alive-for-google/lhobbakbeomfcgjallalccfhfcgleinm/reviews?hl=en-US