I can't guarantee it but it appears that they last indefinitely.

I think the reason is that Vmix calls are peer to peer for the most part. The Vmix software is generating the password. The vmixcall website is just playing matchmaker in pointing remote callers to the direction of your system to facilitate the connection. Your vmix software running on your system is then validating the password and connecting the call to the correct input.

I normally work out of a corporate studio doing multi camera switched recordings, green screen, standups, live broadcasts, etc... When COVID forced the company to work remotely, I had to shift to Vmix and remote vmixcalls for many of our recordings that would be going out to the public for product launches and other corporate announcements.
Some of these recordings required 3 guests and a number of producers. We sometimes used up to all 8 vmix call ins. I had to spend considerable time creating multi-view (2 box, 3 box) setups to combine several inputs and so on. One project was a multi-day recording of a series of video interviews.

I discovered early on with vmix that as long as you weren't creating a new project with new vmixcall inputs and never clicked the "change" button for the vmixcall input, the links and passwords never changed.

So I created a sort of template vmix session that had all the vmix call ins, inputs for powerpoints, images, multi-views, video roll ins, etc... Then just used that as a base for new sessions making any changes and modifications as I needed and then saving it as a unique file.

If you want to have unique vmix call passwords for different projects, you can click the Change button for the vmixcall input which generates a new password. Then save the session as a unique file. The other session files will still use the same passwords they had before.

You can always see and reference what passwords and links your vmix session is using by bringing up the Vmix call manager.