This problem occurred several months ago and is happening again today. EMclient keeps downloading old emails from server. I am running POP3 with option to save copy of email on server after download for unlimited time. I have deleted the duplicates and they have returned on the next sync. Anything changed lately?
It may be some database corruption. Close eM Client and run C:\Program Files (x86)\eM Client\DbRepair.exe. See if there is any difference.