Hi,
I am afraid there is no such built in tools since the RDP failure reasons may vary from the authentication or the performance and so on.
According to the examples of some RDP log on related events (probably locate in the RDSH servers), they consists of the whole process of the RDP logon and the possible event ID that might be recorded.
If there are some clues related to the RDP failure in your event logs, you may consider to trigger scheduler task(notification or else) when the dedicated event was created in the RDSH host servers.
Hope this would be helpful.
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Thanks,
Jenny