What does “cease providing” mean? Don’t you have the software? Isn’t the whole point of a standalone program that once you have it, the company can just go bust?
In the context of iOS at least, it has the potential to stop working or lose functionality as time goes on. Compatibility for apps that are not continuously updated is not high on Apple's priority list.
Disclosure: I work for AgileBits, makers of 1Password.
We recently updated 1Password 6 for iOS to work with the new Dropbox version 2 API. Going forward it should be fine until the next Dropbox API changes and presumably that will be a lot smoother than the change from version 1 to 2 that we just did... at least, I hope. We had several people put a lot of time into that transition.
I'm not sure if your comment applied directly to us, but for anyone wondering we tend to update 1Password pretty regularly. We are not at risk of ever being an app that falls on the "not continuously updated" lists I don't think. We were there on day 1 for Drag and Drop on iPad, and day 1 for Face ID. Much like we were there on day 1 for Touch ID and extensions.
1Password for Mac does not depend on Dropbox's API, it syncs directly to the Dropbox folder on the Mac. So as long as that doesn't change it has zero dependency on Dropbox itself.