Perhaps the path for the second child is hard-coded? Open the hhp file in Notepad and check what the MERGED FILES section says. If you can only see a file name, everything is good. If you can see a path as well, this could explain why the search and index are not working.
I'm unsure how you'd get a hard-coded path for one project and not for the other, but it's possible I think.
There was a recent suggestion that a fix for the hard-coded path is to ensure the child chm exists within the master project before creating the merge in the TOC. If you don't want to keep the child within the master project, then the only solution I'm aware of is a double-compile (compile, open the HHP file and delete the path information from the MERGED FILES section, then recompile) each time you generate a final build of the help.
Thank you very much Amebr. Your answer was right on the mark. I think I discovered how the path was hard-coded. I will describe what happened in case anyone else has a similar situation.
Below is a copy of the "MERGE FILES" section of my master project's HPP file. I removed the "!SSL!\Microsoft_HTML_Help\" from "!SSL!\Microsoft_HTML_Help\FOCUS_Utility.chm". But when I regenerated the master project, the path ("!SSL!\Microsoft_HTML_Help\") was re-added to the file name and the problem persisted.
The difference between " Weight_Module.chm" "Deckhouse_Module.chm" and the other merged files is that I imported them for outside of the folder containing the master project's files. With the other files I coped them to the "!SSL!\Microsoft_HTML_Help\" of the master project before I merged them in the TOC of the master. To fix the problem I had to:
remove the projects from the mater's TOC
Remove the line in the "[MERGE FILES]" section of the master project's .hhp file
copy the merged files' chm to a folder outside of the master's folder.
Remerge the merged ( or child) project in to the TOC of the master project and let RoboHelp copy the merged chm file into the masters "!SSL!\Microsoft_HTML_Help\" folder.
Regenerated the master project.