I use the Easy Custom Labeling plugin chose positions of the labels and safe the layer and project for continuing later. When opening again the project, the layer opens but without any objects inside. Is there a reason why the layer is saved, but not its content?
If you are working a lot with the Easy Custom Labeling plugin, I recommend you to install the Memory layer saver plugin. Thus, you no longer have to save the labels in a shapefile and you can easily go on in your labeling process later on. But do not forget to leave the edit session of the layer before you save your project!
Check the source of the layer. It sounds like it is putting them in a temporary file that needs to be saved before exiting, or you need to save the edits on the layer before exiting.