For Each loop: Some items get skipped when looping through Outlook mailbox to delete items

Likely cause: When you do this InboxMsg.Move, all of the messages in your inbox after the one that was moved are bumped up by one position in the list. So you end up skipping some of them. This is a major annoyance with VBA's For Each construct (and it doesn't seem to be consistent either).

Likely solution: Replace

For Each InboxMsg In Inbox.Items

with

For i = Inbox.Items.Count To 1 Step -1 'Iterates from the end backwards
    Set InboxMsg = Inbox.Items(i)

This way you iterate backward from the end of the list. When you move a message to deleted items, then it doesn't matter when the following items in the list are bumped up by one, because you've already processed them anyway.

It's often not a good idea to modify the contents of a (sub)set of items while looping over them. You could modify your code so that it first identifies all of the items that need to be processed, and adds them to a Collection. Then process all the items in that collection.

Basically you shouldn't be removing items from the Inbox while you're looping through its contents. First collect all the items you want to process (in your Inbox loop), then when you're done looping, process that collection of items.

Here's some pseudo-code which demonstrates this:

Private Sub Application_Startup()

    Dim collItems As New Collection

    'Start by identifying messages of interest and add them to a collection
    For Each InboxMsg In Inbox.Items
        If InboxMsg.Class = olMail Then 'if it is a mail item
            For Each MsgAttachment In InboxMsg.Attachments
                If Right(MsgAttachment.DisplayName, 3) = "xml" Then
                    collItems.Add InboxMsg
                    Exit For
                End If
            Next
        End If
    Next

    'now deal with the identified messages
    For Each InboxMsg In collItems
        ProcessMessage InboxMsg
    Next InboxMsg

    'Loop through deleted items and delete
    For Each InboxMsg In DeletedItems.Items
        InboxMsg.Delete
    Next

End Sub

Sub ProcessMessage(InboxMsg As Object)
    'deal with attachment(s) and delete message
End Sub