I do struggle with this from time to time. It’s a loading issue. Refreshing the page sometimes helps. Changing browser can help sometimes as well. But, mostly I found I have these issues in edit mode. if you go out of ‘edit’ (either by clicking ‘done’ or simply not going into edit if you go into the stories from the “stories” option in the publication menu) I have much less chance of getting PM issues.
P.S. you can change your settings so that any reply on your PM also shows up as an email in the account you registered with Medium. It is a helpful work around for time sensitive communication.