Actually I would not understand why PTC should not allow access to the Prime 6 help files.
After all in the link Terrry provided I can read "PTC will continue to provide technical support access, phone assistance and expert input for versions of Mathcad that have reached end-of-sale."
PTC can't distribute Prime 6 because it contains muPad for symbolic calculations which PTC does not license from Mathworks anymore as they replaced it by a free CAS (friCAS/Axiom) in Prime starting with P6. P6 was the first and last version which contained both symbolic engines.
Nonetheless the help files should still be accessible IMHO.
I am not sure if you may be able to re-run the installation file for Prime 6 just installing the local help. Especially if you don't have privileges to access the program directory.
When I installed Prime 6 some years ago I also had chosen to use the online help files rather than a local help. I would have preferred to have both available and being able to use a simple button to switch between the two, but, alas, its a PTC software.
So the help files never were unpacked to my hard disk and I also got this annoying "404: Page lost in the cloud." error message now when trying to access the help.
After reading your question here I searched in my archives and I found a zip file for installing Prime 6 ("MED-60893-CD-260_6-0-0-0.zip"). This zip-file contains a folder "ptcsh0". This folder, among other things, contains an archive file "ptc0.cab" which holds all the HTML help files in English along with the pics and css files, etc.
I unpacked the whole lot from the archive ptc0.cab to the installation directory of Prime 6, preserving the folder structure in the archive. This means that I now have a folder C:\Program Files\PTC\Mathcad Prime 6.0.0.0\Help\en\.... equally as its created when installing Prime with local help.
After restarting Prime 6, the local help was automatically chosen when pressing F1.
In case you don't have access to the installation directory of Prime 6, you may unpack the help files to any folder on any drive you have access to. Then in Prime click the yellow M at the upper left, chose "Options" and then the "Options" tab. Here check "Set the path for accessing Help at an alternate location" and type in the full path to the help files, including "...\Help\en". This should work as well.
Good luck!