Long story short. If you have Firefox 64 installed and Rapise stopped connecting then run Registry editor (regedit.exe) find and delete the key:
What you need is to simply delete this node.
The reason for the issue is a change introduced in Firefox 64 affecting how the registry is read to load an extension.
As of Firefox 64, the 32-bit registry view (Wow6432Node) will be checked first for these keys, followed by the "native" registry view.
An appropriate change to the installer will be introduced in the next fix-release of Rapise.