You could try my answer (or some variation of it) here:
log4net - any filter for logging only the Nth message?
The questions asks how filter frequently occurring log messages so that only every n-th one gets logged (configurable). I proposed using a custom filter implementation that filters messages that occur frequently in a short period of time.
In your case you could ignore messages that meet a certain pattern unless they occur frequently. You might configure a second appender (like email) and use the filter there. In your "normal" log, just accept all log messages. In the "emergency" log, use the filter and only trigger an email when the message pattern meets a certain criteria.
Good luck!