I suppose that a question like that forces us to examine some of our common assumptions. We all talk about "natural resources", but does nay of us have a clear and quantifiable deffinition of what constitutes a natural resource? Anything that exists in nature could be usefull to someone in some way. By this deffinition, so long as physicall substances exist on Earth, there will be natural resources. But once the planet ceases to exist, there will, of course, be no naturall resources on the planet.
I think that some resources will run out, but we will find a way to substitute these. So I don't think that we will ever run out of natural resources as a whole, but we may (in fact, I think we certainly shall) exhaust some individuall resources in the very distant future.
It should also be noted that if and when we refine nuclear fusion (for example) to the point where it is practical to use, coal and/or petrolium fuels may no longer be used because they are more expensive, less convenient, and a greater source of pollution. Once this happens it could be said that these things have been exhausted as resources, not because their supply ran out, but their usefullness. Once they are no longer considered usefull or disirable, they cease to be "resources".