One of my email sub accounts used by a family member is repeatedly being locked bt BT due to suspicious activity.
I have reset this at least 5 times but it keeps happening.
Any tips/ideas ?
Not really anything you can do if it is somebody trying to log in to the account with the incorrect password. It could be a malicious attempt to access the account or it could be somebody simply making a typo with their email address and entering your address rather than theirs.
Are you using a VPN on one or both of the devices making it appear that logins are appearing to occur from different countries at the same time?
Obviously I do not know your daughters age so the following may not be happening or relevant.
Is your daughter checking her email on another device such as at work or using a friends device at any point. It may be that if she is that the device has her username and password stored and when she does use it, it is using the old password and this is triggering the locking process.
If you "gift" the email account to your daughter she would become the account manager and be able to change the email password her self without involving you. It would however mean that you can not access her email account without knowing the password which may be something that you wish to retain
See link about "gifting" email account.