Your comments

I had this same problem, but for me it became easier when I changed the highlight color to a strong contrast (i.e., red) and I can find words much more easily using the side bar with that color. 

I also have been very much enjoying this plugin for highlighting all matches of a selected word (or even phrase). 

This was fixed today in the dev release build 2102.

- The copy command is now recorded in macros

That made it much better. There's weird cases where on some lines in the JSP the scope is " html.text.jsp" instead of just "html.text.jsp" and so it picks up the java one then, I haven't been able to reliably duplicate when it happens, but it does seem to happen most often if the code is a scriptlet all on the same line (not the expression evaluation kind <%= %>) and my cursor is inside a if statement, but not always. Thanks for the help though Jon, this is certainly livable.

I think Micah hit it on the head, there is too much potential bloat/slowness with such a feature. I can see someone making a plugin for this if the api allows it, but definitely not in the core.
I do this all the time too on accident. I didnt even know pressing ctrl-f again closed it! If i want something closed I always press escape and it does the trick just fine. SB2 is even smart about which one to close first if there are multiple things open. (such as ctrl-f then ctrl-r). 

I just realized though that as long as the focus isn't on the search bar when you press ctrl-f, it does indeed go back to the search bar without closing it.

Found my own answer after 3 months (forgot I had this account). Scope is controlled by each languages .tmLanguage file in the Packages folder. At the bottom of the .tmLanguage xml file is a key called scopeName with the scope just below that. For jsp it isnt source.jsp, its text.html.jsp.
I'm using windows 7 build 2032 64bit, but I also tried it in build 2039 with both installed and portable versions and it still does it, at least in a newly created file. I wasn't able to duplicate it in an existing large JSP i was working in with ctrl-z, but ctrl-u seems to always undo it.

edit: found out how to duplicate it with ctrl-z, type some characters, then make a bookmark, then type some more characters, then hold ctrl-z and it will delete the characters and the bookmark.