Just a couple of days ago I made a blog post, and about half of it was dealing with this question: http://www.economicsofbitcoin.com/2013/03/the-classification-future-of-bitcoin.html
EDIT: basically, since a new network is not compatible (just see the recent block size hardfork debate) it is a question of network effect. If the network effect is strong, competitors will have it more difficult to take away market share from bitcoin, and have to present a compelling reason to switch. Economists tend towards the position that money has a strong network effect. In a cryptocurrency world, a competitor would have to spend a lot of money on the infrastructure, such as software libraries, documentation, PR, merchant integration, and provide liquidity on the exchanges. Probably also on lawyers.
An analogy that I often use are languages or the IP (protocol). It also is easy to create a new incompatible standard for these, just the idea that one day you wake up suddenly everyone uses something else is implausible. IPv6 has existed for 20 years now, and still hasn't replaced IPv4, because there is so much infrastructure that's not compatible and people don't want to spend money on replacing them. That's not to say that a switch cannot occur, just that it takes time and resources. I expect that eventually, IPv6 (or its successor) will replace IPv4. The IPv6 share of network traffic has been rising.
Eventually, Bitcoin may also be replaced by some other alternative that people find better. So far, that doesn't seem to be happening. The only alternative that seems to have a shot at all so far seems to be Ethereum.
For a reference, look at https://coinmarketcap.com, where hundreds of competitors to Bitcoin fail to gain non-negigible market share.