What is the ruling on my fiancée's action of asking to break off the engagement for simple reasons, after repeated private meetings between us, knowing that we are regretful and repentant and wish to complete the marriage?

We regret the forbidden relationship between you two, and we praise Allah for your repentance. To find out the reason for the breaking off of the engagement, you can delegate a female relative of yours. If the girl insists, then be patient and seek reward from Allah, for perhaps there is good in that. Seek guidance from Allah through Istikhara and ask Him for success in a righteous marriage. Beware of weakness in faith, which leads to despair or indulgence in forbidden acts, for everything is by divine decree, and Allah will prepare good for you and grant you success in a happy marriage.