We have a very basic Flow in place. When a new email arrives in a dedicated mailbox all attachments are saved to SharePoint and the email moved to a sub-folder.
This flow works MOST of the time, however perhaps once or twice a week the flow will simply not trigger. The only way to get it to trigger is to forward the email back into the same mailbox, at which point it usually then triggers successfully.
I haven't been able to intentionally reproduced this issue, but as noted it does happen once or twice per week.
I have a similar issue. When a message from any of several addresses arrives with an attachment whose filename contains a certain string it saves to Box.com. Most of the time it works, but sometimes, normally a few times a week, it does nothing. The flow doesn't trigger and fail, it just never starts. There is no record in the run history of the email being checked for the conditions.