Well, like anything it totally depends on the specifics.

A modern B+W film, properly fixed and washed, is essentially forever. Metallic silver doesn't really degrade by itself (50+ year lifespan) - and you can use a toner like selenium to convert the metallic silver into silver selenide which is even more stable, easily 100-200 years+ (note that this is generally done with prints but it also works with film).

Color films are generally considerably less permanent because you can't capture color using metallic silver unless you have one negative each for red, green, and blue. You can do that though, the TechniColor "3-strip" process did this and it's actually extremely stable for its time. It was also used for the color series of Magic Lantern glass plates from the Prokudin-Gorsky survey of 1905 [0].

Modern negative films are decent if stored properly, but early color negative films were pretty disastrous in terms of long-term stability.

Color slide films in particular are actually quite decent as long as you store them properly (cold, and out of light). Kodachrome (K-14 process), in particular, was remarkably stable because there is actually no dye in the film itself - it's created by reaction during the (incredibly complex) processing, so (again, if properly washed) there is nothing left to continue reacting and "fade" the image out. Properly processed, Kodachrome does actually approach the stability of B+W film. The only thing that really degrades it is exposure to light (i.e. projecting it or leaving it in a window).

Many early film bases were problematic though, because it was essentially a parallel effort with basic materials-science research in plastics. Nitrocellulose is super flammable and many early theaters burned down as a result, it was replaced with acetate "safety film" which tends to go vinegary, finally everyone settled on polyester. Nowadays you can have a pretty good expectation of the storage properties of our plastics.

Anyway, to make a short story long - you are assuming the question by adding "a well-thought-out digital archive". You can't pick a random instance of film storage and pretend that's representative of a modern, well-thought-out effort at archival. People did all kinds of dumb things in the past - South Carolina's constitution is falling apart because they laminated them back in the 60s and now they're turning to vinegar too [1]. The equivalent in digital terms is a random paper tape from the 60s pulled from someone's attic, or a DVD that was scribbled on with an alcohol-based marker and left on a spindle somewhere. Or someone's VCR bootleg of the first rough-cuts and rotoscope layers of Star Wars (see "Deleted Magic" [2], it's amazing but wow is the quality terrible in some of them).

It's always going to be possible to store some relatively stable physical media, that's the easy part. The problem with digital is you then add additional tasks of loading and interpretation on top. Even if it's stable, how do you get that Quadruplex video tape into your computer? Is there a driver that interprets the filesystem? A codec (ideally open-source)? Is there a sync signal in the medium that might degrade (like VHS)? etc etc. Yes, these are not insoluble problems, but they do add a huge threshold to get over. It might be worth doing to save Star Wars but it's not going to happen for Uncle John's photo collection.

Consider something like the task of encoding a message to an alien race. You have to provide something like a Rosetta Stone to help make sense of your format. Or you could just send a phonograph which can be read by many different methods (laser measurement is the coolest). It's a pretty solid assumption that there will always be basic instruments for physical measurement like lasers and reflectometers, and that's all you need to interpret a basic medium like B+W film or a phonograph. Although I suppose how dare I assume the visual wavelength of an alien species! /s

On the other hand - if you are going at it thoughtfully, i.e. periodically rotating your digital storage medium to whatever the standard is at the time, and you retain sufficient backups - the chances of there ever being a total discontinuity in migration path, or a total loss of knowledge on how to interpret the format is relatively low. The going at it thoughtfully part is the key though. Again, nobody apart from a handful of archival specialists or enthusiasts can really read a random minicomputer tape from the 80s, and that's only 30 years.

I personally started noticing bit-rot on a significant fraction of DVDs that I burned within 5 years (at least 20% of discs). Now I use DVDisaster to encode extra parity/recovery data on a rolling basis - disc X contains a 20% parity file for disc X-1, with the most recent kept on my HDDs, so that I can "chain" backwards through them.

Still though - imagine the kind of digital files that were made in 1995 with MOV files or whatever. Now compare them to the high-resolution 4K scans that are made from the same films. That's really another problem with digital, not just archival - the bits are what they are, you can't go back and try again when technology is better.

[0.0] https://www.flickr.com/photos/prokudin-gorsky/

[0.1] https://www.loc.gov/exhibits/empire/making.html

[0.2] http://www.loc.gov/pictures/collection/prok/

[1] http://www.npr.org/2017/02/21/515410087/an-attempt-to-save-s...

[2] https://www.youtube.com/watch?v=f2r4Nffrc6Y (there is also a Deleted Magic Revisited DVD with better quality and some more footage - finding it is left as an exercise to the reader)