In ASP.NET WebForm usage, If the AdditionalDataItems collection is set in Design Time (i.e. Visual Studio property editor or directly within ASPX markup), then, this data is not persisted. But if you set AdditionalDataItems from Code, then, that works fine.
Possible work arounds
Please set Additional Data Items from Code. For example, set it from the Page's Load Event hanlder method or programmatically from any post back event handler method. Do not set this collection in DesignTime.