The inbox does in fact have different operation to other folders so it fits that you only have this issue there. Someone else will likely post later with better ideas but my first thought is that you don't have Delete permission to the inbox. So Pegasus is moving messages as requested but then finds itself unable to delete the original from the inbox, causing that file to reappear upon the next check.

Use Help > About > Info and look for the New Mailbox Location to find which folder's permissions you need to check.

Good day.  I am using Pegasus Mail Version 4.63 (Win32) build 325 (Windows XP and Windows 7 - tried on 2 different machines and get same result using Mercury as Server) and have noticed that I cannot (permanently) delete anything from the Inbox.

To qualify; I can delete and the message(s) seemingly disappears from the Inbox and duly shows up in Trash however after a few moments the "deleted" messages reappear in the Inbox.  The same happens when I Move a message which I suppose is a similar operation?  The Message appears where I want it to go but then also reappears in the Inbox a few moments later.  I only see this phenomena on the Inbox folder and all other folders work as one might expect.  Oddly, I cannot find mention of a similar problem anywhere but I further cannot imagine that I am not the only person using Pegasus on planet to have this issue.  Surely I do not have to go back to using the diabolical (and seriously wobbly) Thunderbird do I?  Help!  Thank you.