With the previous version of Find in Page I was able to highlight all of the occurrences of a string and then do whatever I wanted on the page and the strings would stay highlighted. The current version turns off the when I right-click in the page.

This is indeed different, but there needs to be a way to hide the dimmed background when you interact with the page. Indeed, there are interactions upon which we shouldn't hide the highlights, but these are already tracked in bug 1291278.

I disagree with the decision, as this new version causes highlighting I want to go away on me several times a day. But I am more concerned with the inconsistent behavior around when the highlighting goes away. I've been using this feature regularly and I don't know what actions cause the highlighting to end. For example, on the eBay watch list items have options "Delete item" and "Add note" (or "Edit note" if a note exists). Left-click Delete item and you exit search mode, but left-click Add note and you get a sub-window and can type and save a note and still remain in search mode.

Well, all I can say is that bug 1304073 makes sure that a whole bunch of scenarios that currently make highlighting to disappear will not be anymore. IOW, it'll be a _lot_ closer to the behavior you'd like to see.