you say you "renamed" the old alias -- can you  be more precise? the filename has no effect on the search match.

In the cpanel alias file, I opened it in notepad, renamed the old alias, and added in the new one, i.e. the name before the first | in the entry.  I'd already noted that I didn't have it when I searched in FARR, and after it, I did.  But the old one still didn't show up.

In my cpanel alias edit dialog (the read only dialog in FARR) I have the following two entries now:
Old Network Connections | %windir%\system32\control.exe netconnections /ICON=NetworkSharing.ico /winvermin=5.1 /winvermax=5.9
Network Connections | %windir%\system32\control.exe ncpa.cpl /ICON=NetworkSharing.ico /winvermin=6.0 /winvermax=6.2

Only the second one shows up.

Thats because of the winvermin and winvermax -- they tell FARR only to show certain items depending on the version of windows.

Ah... that makes sense.  Well, the one that I have titled 'Old' was the one that was in my install.