If you consider you have Click A through Click E, plus your Do-more...
EVERY device on the wire must process every message put on the wire. So even when Do-more and Click A are having a conversation, Clicks B-E receive and analyze every message to determine whether they need to act on it. They have to process each message (even if just throwing it out) and doing so takes time.
The issue you're running into is that the time delay between a Click A's last transmission and Do-more transmitting its first message to Click B is too short. Do-more can fire off the message before Click B has finished throwing out the last message it received from Click A. Click B misses part of the first message from Do-more.
The 10mS delay would be a good way to fix it, but adding a delay to the stage should also work without slowing down ALL the traffic.
The scan time of your Clicks should play a roll in this too.