For IMAP accounts eM Client by default only downloads the headers of incoming messages and the body content is downloaded once you open the message's details.

While the startup synchronization is being processed by your server, it's possible the request for downloading body content may have timed out and can be run again once the folder sync is finished.

To avoid this, try to enable the "Download messages for offline use" on your account or one of your folders – for example, your Inbox.

To do so, navigate to your account settings, IMAP, and check the option to download messages for offline use, or right-click your folder, navigate to its properties and enable the option for selected folders only.