It asks for password because the shares probably are mounted with only root permission. Mint uses sudo to perform root/admin tasks, and at reboot the password cache for that purpose is cleansed as a matter of security policy. I don't tick "Remember", neither "Forever", but you can make your choice, depending on personal taste and condition.
It is a matter of policy and frequent asking for password is the default. You can change or eliminate the need for sudo (password) by changing the ownership and permission of mounted shares.
Hope that helps. Good luck.
Last edited by malekmustaq; 12-19-2012 at 10:52 AM.