20-Year Prospect
Computer animator jobs are expected to grow in number, though not as quickly as you might expect for a career that seems to be featured everywhere these days (source). It's true that we've seen an increase in animated media making it to the mainstream, and new special effects requiring cutting-edge animation are being developed all the time.
However, studios often save money by outsourcing animation work overseas, and that isn't expected to change radically in the coming decade.
The growth in the industry might not be as speedy as you'd like, but it seems like a sure bet that movie studios will keep churning out films that require extensive computer animation. There should also be no shortage of video games requiring the same. Keep following your computer animation dreams; there will still be a sizeable industry for your skills twenty years from now.