Can you expand on the fragility issue? Are you talking about the lack of chargebacks/reversing transactions?

There are two aspects to it:

As epaga points out, if you lose access to your wallet (forget password, hardware failure without backups, somebody dies without leaving the password to their heirs) there is no way to retrieve that money.

Secondly, if a transaction is made to a valid-according-to-the-protocol address that nobody owns, that money is lost with no possibility of getting it back.

You could argue that these are problems that can be solved with more technology on top of Bitcoin, so you could have Bitcoin banks that:

1) Guarantee that your wallet is stored securely. The idea is that you need to trust that the bank is better at not doing stupid things than you.

2) Control access to it. Like modern banks, you would need to trust these banks, for they would have access to your wallets.

3) Make sure that payments are going to the right place. To make a payment, the bank that controls the wallet that the payment is being made to could be required to notify via another protocol that the address is real and belongs to a certain person/organisation. If this was widely used (so that payments to raw addresses was considered dangerous), it would also prevent a hacker from breaking into, say, EFF's Twitter account and tweeting "we're now accepting donations on this address...".

Re 3: I've been reading about contracts and script in bitcoin. Apparently you can setup transactions such that they automatically roll back to the originator after some time. Might it be feasible to use this to avoid the 'valid address/no wallet' problem? Establish on transactions a period of days/weeks in which the destination has to complete the transaction. I haven't had a chance to wrap my mind around it yet. Need to free up some evenings to spend on it.

If you lose access to your Bitcoin address (e.g. by losing your impossible-to-guess password or deleting your private key), the Bitcoins in that address become completely unreachable. This means you theoretically could wipe out your entire life savings with the click of a button and no one could help you retrieve them.

In (not only) that sense, Bitcoins have more in common with hard dollar bills than with bank funds. If you burn your dollar bills or lose them in some other way, they are gone forever. Similarly, it is not possible to duplicate a dollar bill. In this regard, Bitcoin is even more secure since forgery is not possible either.