I am not sure I'd want you as counsel😉 Why do you think they have a right to refuse a refund just because a contract term has been broken? What a strange conclusion to draw.

In England and Wales (and similarly across Europe) this type of term would be covered by UCTA and retention of prepayments on consumer cancellation is one area the Office of Fair Trading don't like. If I were involved, I would be pursuing them. Becomes more complex if using VPN etc. when entering in to the agreement!

Btw, the Eharmony T&Cs are meaningless: they agree the law of England governs them but they use terms such as "Felony". As is so often the case with Online companies, they have copied and pasted their US T&C to their UK website with no thought which makes enforcing them very difficult as they don't mean anything in English law and are usually full of terms that would never get past an English judge.