We don't say solar is non-renewable because using every single available bit of solar today has no impact on the solar energy available tomorrow. This is not true of nuclear, even if you increase the total quantity of available fission-derived energy by 50 or 100 or whatever the outer estimate is for breeder reactors compared to non-breeder fission.
Based on the math in this paper[1] there's enough uranium floating around to keep the planet running on the order of hundreds of millions of years at modern energy consumption levels. The price of the material would go up compared to what it costs currently, but the raw material costs are a small fraction of bottom line anyway.
[1] http://large.stanford.edu/publications/coal/references/docs/...