Plastic film caps are very stable and should never 'need' replacing. You can of course replace them if you believe alternatives to be sonically better but that is a different issue.
Electrolytics do drift out of spec but there is no easy rule of thumb as it will vary between brands and even batches.
IME it isn't the capacitance value that usually drifts but the ESR - and that is likely to be far less of an issue in a loudspeaker crossover than in a PSU. That's because the drift is usually very modest inside the cool working environment of a loudspeaker.
So for example if you have a fresh cap with 0.05 ohms ESR and it sits in series with the 8 ohms of a tweeter, if it drifts up to 0.1 or 0.2 over a decade or two - well don't worry about that!
You also need to take great care when replacing electrolytics in costly, vintage speakers as the design team will often have used fine component selection and perhaps even tweaked individual crossovers to meet a tight response specification. The BBC designs fall into the category but so do many others. It would be unwise to simple start cap swapping in those designs without access to test equipment.
13 year old Missions can be safely left alone.
Worth noting that many speakers, particularly at the budget end will be using +/- 10% spec caps in the crossover (and i've seen 20%) which is food for thought when contemplating the re-cap of a less than youthful loudspeaker.
I doubt that - If they used modern polyprop caps etc.
I am use ~30-40yr old 15" Tannoy crossovers, one pair with fairly modern looking caps the older pair less modern but plastic bodied caps all the same and they sound as fresh and lively and accurate as you could wish for.
I also have some 30yr old Mission 700 speaker in the garage and they sound as good as they did back in 1980.
You could be unlucky though I guess...
Good little speaker the 700 - we need something like that today for reasonable money.
Similarly I picked up a pair of Dynaco A25s last week that were manufactured in the early 70s. Superb sound and re-caping them isn't particularly high on my agenda.
