That is exactly what I'm testing including the reload of the Rig. Stored changes stick. No issue here.
Perhaps you don't replace the original Rig, but store a new Rig and then reload the original.
Please share a demo video.
I figured out the issue, if you hit store to save the changes it works as expected. However I alway change the tag by using the return key to issue the save command and this is where the issue is. This is when the rig is in the profiler and loaded in the buffer.