It wouldn't stop the RRD, no. But since 1, 5, and 6 are running, that suggests the RRD is not stopping/failing on 2, 3, or 4. My next thought was that there could be a problem with the underlying report.
Are all the actions different reports or the same report to different addresses?
Here's what I'd do next. Make a copy of the RRD and open it in Notepad. Remove all but the first seven actions. Open it in Solution Builder and set each action to email to you, and uncheck the Suppress If No Records box. Now execute the copied RRD. See what happens with 2, 3, 4, and 7. It might give you some clue as to what's going wrong.