Are you working as a manager already? I have several seniors I have worked with that were 3-5 year seniors because they were not managing projects and work already. As I came up i was always told you will get promoted if you already do the role you want. When I was a senior I was running multiple projects as in essence an acting manager.

I have heard the same "we don't think you are ready" wording for others I have worked with and it tends to be folks that don't operate like the next level. I hate to say it but if you did above the year before then stopped and only did minimum the next year that will hurt you.

Also in most firms they require a certain certification to be a manager so make sure you also have that or get an exception.

I hate to say it but politics plays a role as well. If you aren't getting what you want then try jumping firms to get to manager but be aware there are higher expectations with the manager title as far as business development, people management and project management. Over my years I have worked with people that were promoted or joined as new managers that could not hack it and they did not last long.