If film actually lasts that long, then why not print a digitally-encoded film? (Think full-frame QR codes or how Dolby Digital used to encode digital audio between the sprocket holes.) Sure, the film would probably be longer than a human-visual print, but then the encoding could include forward error correction. Don't use inter-frame compression (so that one part of the movie is independent of another), and for that matter don't get creative with the intra-frame compression--just use RLE or something really easy to reconstruct.

Also, when printing such a digital film, be sure to write down the encoding algorithms on archival-quality paper, and store that along with the film. ("We sampled an 8192x4096 image in anamorphic ratio X, with three channels, 16 bits per sample per channel planar, over the color space Y...")

As with all such things, if people were serious about it (or money becomes involved), this would be a solvable problem (or at least a tractable problem).