Currently although build parameters are re-used not re-using certain build environment variables can easily cause a rebuild to fail. As a result, I suggest to include an option to allow a re-build to use a set of the environment variables from the original build.
A use case similar to JENKINS-13647 is the Parameterized Trigger Plugin which sets predefined environment variables for a downstream project before triggering a build. When such a downstream project is re-build it typically fails, as although the build parameters are preserved, the predefined environment variables are not. Otherwise this is a great and extremely useful plugin! Thank you!