Please note that billable and labor rate updates are never applied to locked, approved, or invoiced logs.
Such logs will have a lock icon displayed here:
If you put your mouse cursor over the lock icon, you will see the reason for the time log being locked:
To be able to update the rate on invoiced entries, you need to delete the related invoice draft/invoice first.
To update the rate on the entries that are in a locked period, you need to turn off the period locking setting.
To update the rate on previously approved entries, you need to reject them first.
Once the entries are unlocked, you need to update the rates again for the new rate to be applied to existing time logs.