1) The promotion was not applied to one particular transaction. I am unable to point out why this happened.
Is it a coupon or a promotion configured to apply to all purchases? If a promotion to apply to all purchases be sure to review carefully the conditions you've configured for it.
2) I need to now apply this promotion to the above basket. How can I do it from the administrator? (I don't want to hassle the user further for issues due to the system)
You can't apply promotions from backend, but you can cancel their basket then go through the basket process for them on frontend while logged by visiting their profile and using their Subscriptions tab as normally.