Whilst working with a vNext Release Management pipeline I started seeing the error
New deployment is not allowed as an another deployment is in progress.
Retry the deployment after sometime.
Problem was I could not see any blocked or paused deployment releases. All Internet searches mentioned multiple pipelines that share components, but this was not the issue.
Eventually I found the issue, my release pipeline included a step that ran CodedUI tests via TCM, hence a previous running of this template had triggered the test via TCM, but they had stalled. I found this by looking in MTM.
Release Management was just saying the release was rejected with the above error message, no clue about the unfinished test run. Not that helpful.
You might have expect Release Management to return only after the test had timed out, but that is only down to whether you set the release pipeline to wait or not, I had set mine not to wait.
Once I stopped this test run via MTM all was OK.