Hi David,
I apologize for the frustrations.
Credit card companies employ a system called 'trusted vendor' or similar, where a recurring subscription will automatically use a new credit card number should the original one be cancelled, and the account itself is still intact. If you do not agree with this policy you may contact your credit card company for more information.
If you still need billing help, you can use this phone line Monday through Friday during normal business hours ( Long Distance: +61 2 9158 3272 ), and please let us know if it should fail for any reason.
We also offer case creation through this support article online: https://support.logmeininc.com/central/help/how-do-i-contact-support
