Create a simple multi-configuration job. My simplest example that demonstrates this bug has just one user-defined axis, and its build steps do almost nothing (I first saw the bug with a much more complicated job, but I have now found that it happens just the same with a really simple one).
Save the job configuration. The job can now be used as normal: you can run builds, and you can look at the builds in the list, and so on. Everything seems to be fine.
Then reload your Jenkins configuration from disk (or, equivalently, restart the Jenkins service from the Windows control panel). The multi-configuration job is no longer present in the list of jobs! If you look at the Jenkins home directory, you'll see the directory structure that Jenkins created for the job, but you can't see any sign of it via the Jenkins user interface.
I have tried this several times with different settings. It always fails.
This is with the current release of Jenkins (version 1.474).