This is because the project might have exceeded the contract amount and the time entry evaluation has kicked in. As the amount spent on the project exceeds the contract amount, you are prompted and the time entry's billable status is automatically adjusted to non-billable. You can continue to log non-billable entries, but have the option to change their status to billable manually. You can prevent this by applying the project rule 'Skip time entry evaluation'. In that case, BQE CORE will stop flagging the time entries as non-billable.
This can also happen if you have set the project's Contract Type to Marketing or Overhead. By default, BQE CORE marks all time entries of the projects of these contract types as non-billable. If this is the case, you should update the contract type of the project in order to bill time on that. CORE prompts you to mark the existing entries on such a project as billable when you do so.