I sent BTC/XCP/TOKEN a while ago, but the transaction hasn’t gone through - why?

Unfortunately it’s not possible if you’re not in possession of the private key.
Of course if anyone could “do something about” some bitcoin address that’s not theirs, it’d be crazy.
If the address is at an exchange, you can write to their Support and they may be to help although they would have to run through special and troublesome internal procedures and it may take a while, but at least theoretically it’s possible.
They could sweep the token with the private key of their address and send it to the right address at their exchange (or back to you). It’s quite an effort for someone to do that at crypto exchange (since the person who would help you would have to get the private key of the hot wallet for the exchange) and if their rules may prevent them from entering the private key into any 3rd party software (but that’s required if you want to extract Counterparty tokens from a Bitcoin address) so … yes, it’s a lot of trouble.