To summarise the reasons why payments fail when a counterparty is offline are:
1) transactions require the signature of both parties, and obviously won't work with just one signature
2) the transactions are relayed directly p2p, and there are no other nodes that are involved to store transactions
I know how it works, my point is, I have doubts it can catch up at mainstream level if you can't make a transaction at any time, since you would need to contact the person that you are sending coins to first, to guarantee that it's node is online, this seems archaic and annoying.
For big businesses it shouldn't be a problem because they will have nodes online 24/7 but p2p will require contacting the person first which sucks.
Why would this be such a big problem? When I receive a payment by bank, I need to be online too, to confirm that I received it. More people than ever are online 24/7, and I doubt this will ever go down again.
You don't need to be online to receive a payment in a bank... since when would you need to? For example, one can be receiving payments from rented properties in your bank account without even talking to the people paying you for months. Looking at your funds to see if you received the payment is different from having to be online waiting for a transaction to arrive because otherwise it will not.