Yes, I believe that there will always be people making and believing in open source software. Not every person who creates something is in it for the money. Some people just want as many people as possible to have access to a product that they believe people should be able to own or play. Making things open source makes that dream much easier.
The Open Source movement is based on the commitment of some programmers to make information and resources freely available to anyone who wants to use it. In actuality, this is a form of activism and it is, as such, alluring because it can be effective while involving an activity (programming) that is fun. Open Source projects include various ways of providing third world access to technology. Because of this, Open Source is here to stay.
Open source software will last because it is usually free or very low-cost. In the state of the economy as it is in the United States, a lot of people are short on funds. And if there are companies who create software like this for free, then the public will eat it up -- especially if it is useful software.
I think open-source software will increase in usage as more and more small independent developers are making software nowadays and most of them make it open source, I think open source is a fantastic tool since it lets those with ideas for different uses of the software be able to modify it to fit their needs.