Do not have the xbox live

Go to settings/accounts/remove accounts. Remove the profile that is having trouble accessing Live.

The go to setting/account/family/add to family.

Make sure the account that has gold has the console set as their Home console.

The only way that can happen is that their xbox subscriptions has ran out

its also a way that xbox makes its money since usually at the start they sell consoles at a loss to make up for it with games and xbox live hope this helps you can also pay for a year if you wanted to or even monthly

Hi John,

Xbox Live is a subscription service which allows you to play games online against other people. You don't have to have a subscription if it's not something you need. Xbox Live gives you the ability to play against others online, make full use of online features
on certain games. You also receive a number of free games every month or so.

As well as a yearly charge, you could pay every three months or every month. It all depends on what suits you.

You can get more details on billing and payments for Xbox Live here