I would propose functionality to be added to the Bitcoin's protocol that allows storing payment details in the Bitcoin's block chain for a month (or some other period of time). When the payment details expire nodes can purge them from their copy of the block chain to save space. The merchant has 30 days to turn on their bitcoin node and fetch the payment details from the block chain. Those details should be signed by the payer's private key and encrypted with the payee's public key.
I think that is a good idea, but the problem is that in the initial payment request, the merchant has no way to know who (identity or bitcoin address) is sending them the bitcoin. They should definitely sign the request, but encrypting it is not possible without knowing the other party's public key, which is hard to know without knowing who is paying and public keys are not revealed until they sign a transaction.