External mail source with 32-bit MAPI client

Sorry to hear that.
Knowing that it can work you need to analyze what could prevent it from working in your configuration.
Windows eventlogs may give you a hint. If not, then check that firewall on the server as well as on the edge to WAN allows traffic on the port used. Check that your configuration in the M-Files mail source settings is correct and that the username and password actually will allow access to the external mailbox via another client (web access, Outlook or other mailclient) - if possible test directly from the server.
Perhaps your mail source settings are correct but your metadata settings for M-Files somehow prevent the new documents from being added. Recently I had a case where I tried to place documents retrieved from a mail source into a document class with a workflow that so far had only been used for manual addition of documents. The first step in the workflow required users to add certain metadata before the document could be saved. The external mail source could not add these metadata and therefor the document could not be saved, so a change in the workflow and metadata settings was required.
There are many more examples of things that can go wrong. You need to analyze the path all the way from your external mail box to the destination in M-Files. There is no way we can help you and pinpoint the error without you getting into the details.

Sorry to hear that.
Knowing that it can work you need to analyze what could prevent it from working in your configuration.
Windows eventlogs may give you a hint. If not, then check that firewall on the server as well as on the edge to WAN allows traffic on the port used. Check that your configuration in the M-Files mail source settings is correct and that the username and password actually will allow access to the external mailbox via another client (web access, Outlook or other mailclient) - if possible test directly from the server.
Perhaps your mail source settings are correct but your metadata settings for M-Files somehow prevent the new documents from being added. Recently I had a case where I tried to place documents retrieved from a mail source into a document class with a workflow that so far had only been used for manual addition of documents. The first step in the workflow required users to add certain metadata before the document could be saved. The external mail source could not add these metadata and therefor the document could not be saved, so a change in the workflow and metadata settings was required.
There are many more examples of things that can go wrong. You need to analyze the path all the way from your external mail box to the destination in M-Files. There is no way we can help you and pinpoint the error without you getting into the details.