I've had really good results with using archive.is - Just throw that in front of a link with a forward slash and you're good to go.
Like archive.is/https://example.com/
Never had an issue yet. There was one time where a page looked a bit weird on my phone, and I couldn't see the very last paragraph of the article. But enabling desktop mode in my browser fixed it.
When no one has saved a snapshot yet, it asks me if I want to, and I tell it yes, and then it creates a snapshot, and I can see the site. Is that what you mean, when you say it fails? That you have to say yes to it making a snapshot?