¡Hola!

This is by design, from https://blog.mozilla.org/futurereleases/2015/10/08/npapi-plugins-in-firefox/ :

"since new Firefox platforms do not have to support an existing ecosystem of users and plugins, new platforms such as 64-bit Firefox for Windows will launch without plugin support."

The code is the same on 32 and 64-bit Firefox.

I believe you could install both 32 and 64-bit Firefox on the same host with no major issues.

Let us know if this solves your question.

¡Gracias!

The 64-bit version of Firefox on Windows is in its infancy and plugin support is extremely limited at the moment. That may improve over time, but I really have no idea.

You posted with Firefox 45 -- is that "Nightly"? I have read that Nightly normally uses a different profile folder from the regular releases of Firefox so that you can switch to Firefox 42 (or beta, or Developer) without having corrupted settings. However, having never done it myself, you might want to wait and see what comments you get from other users of experimental releases.

DonJoyceWard said

Must I go back an use the considerably older Firefox that is still in 32-bit code?

The current Firefox 42.0 (Win32/Win64) Release is not older. The Firefox 45.0a1 Nightly builds you are Testing is in development and not even close to Release. Release < Beta < Aurora (developers edition) < Nightly

If you wanted Win64 Firefox then there is Win64 Firefox 42.0 Release however it is not so public on mozilla.org https://archive.mozilla.org/pub/firefox/releases/42.0/win64/

The Win64 Firefox 42.0 only has the 64-bit Flash Player white listed. The upcoming Win64 Firefox 43.0 Release looks like 64-bit plugin Silverlight will be white listed.