I think about this a lot... what will happen to the network once close to 21m BTC have been mined. There is no reason to carry on mining and supporting the network.
The transaction fees will be a reason to continue. But I don't know if this will attract a large group of miners (at least not as many as now). And if that is the case, the computing power on the network* will decrease, making an attack (fraud) more likely.