So cheat! If you use a physical calendar, you can mark those days with another symbol, like an arrow to show that the chain carries on. If you use an app, you can mark the day anyway, knowing that you had a legitimate reason to skip it.

Think of all the benefits you would get from practicing 95% of the days marked, compared to a much lower percent without the chain. Don't let the 5% or 1% stop you.

As an aside, this is my view of veganism. When I talk to people who say they can't go vegan because they'd miss cheese too much, or kebab, or whatever, I suggest they go vegan and keep eating cheese or kebab. 95% is a lot better than nothing!

That said, I can't do chains. I get anxious after a while carrying a long streak, and will either conveniently forget a day and mess up the streak (and feel relieved), or decide during a streak that I'll stop at 30, or 100, or whatever, just to give me permission to get off the treadmill. I don't like when enjoyable things turn into a chore.

Some apps are nice and let you go back and add marks even if you forgot to do it on the day. Some apps, like Duolingo, let you unlock tokens that protect your streak if you miss a day. But some apps are really strict, which can be annoying if you finish something after midnight and realize that you just broke the chain. My wife had that with a writing app where she finished exactly at midnight, which counted for the next day and her streak was broken.

So if I did a chain, I'd use a text file, or a paper, or send myself an email a day logging that I did the task. I wouldn't trust an extremely rigid app, because, as you say, there can be legitimate reasons why you miss.