My machines were recently upgraded to Google Earth Pro version 7.1.8.3036 and it broke the ability on one of them for a BaseCamp route to be displayed in Earth Pro.. only on one of the machines. Since one computer still works fine, that implied Google has done nothing further in their newest code version to break the link.
After redoing SUSSAMB's recommendation below from one of his earlier posts, all is well again.
From the Command Prompt type the following as applicable and press ENTER:
(Make sure you are in the C:\ root directory)
"C:\Program Files (x86)\Google\Google Earth Pro\client\googleearth.exe" /RegServer (works with Google Earth Pro in Win 7...10)
"C:\Program Files\Google\Google Earth Pro\client\googleearth.exe" /RegServer (Google Earth Pro in XP)
"C:\Program Files\Google\Google Earth\client\googleearth.exe" /RegServer (Google Earth in XP)
"C:\Program Files (x86)\Google\Google Earth\client\googleearth.exe" /RegServer (Google Earth non-Pro on Win 7, 8.x and 10)
Note for those not used to using the command line in Windows, the double quotes in all of the examples are critical.
They MUST be there and in the indicated places or you'll get an error that the directory name is invalid. It won't harm anything; it simply won't work.
If you want to upgrade to the latest version of Google Earth, or Earth Pro go to this URL https://support.google.com/earth/answer/168344?hl=en