First of all, if you have any security software installed (e.g. Avast, AVG, etc.), please make sure that the program itself and its database are both up to date.
If this does not help, then try completely disabling your security software (at your own risk) or make an exception for the JuiceboxBuilder executable file to see if this makes a difference.
We've had a couple of Avast users report similar symptoms to those that you describe. However, I contacted Avast and they say that they cannot replicate the problem with the latest version of their software (v18.3).

If this does not help, then, with JuiceboxBuilder-Pro closed, please check to see if the following folder exists on your system:

C:\Users\Username\Documents\JuiceboxBuilder-Pro\.tempGallery

If there is a .tempGallery folder in this location, please delete it manually.

The .tempGallery folder is created automatically by JuiceboxBuilder for internal use only (for the live preview window and as a temporary gallery folder until the gallery is saved on the 'Publish' tab).
It should automatically be deleted by JuiceboxBuilder-Pro on closing the application but, if this fails, it has been known to render the 'New Gallery...' and 'Open Gallery...' buttons inactive.

The only way that I've been able to replicate the symptoms that you describe myself is to save a gallery to a Google Drive folder (so I'd recommend not saving a gallery to a location which is being synced to an online file sharing service) and the problem seems to be due to a persistent .tempGallery folder (which has not been removed as expected).
You may not be using a Google Drive folder but a persistent .tempGallery folder might still be causing a similar problem.

Hopefully my notes above will help.