When multiple files are open in tabs, switching from tab to tab loses the search context immediately, replacing the current search with an out-of-date search, ie. the one last used on a different tab. To continue the current search, you must have already copied the current search into the copy buffer then you have to paste the clipboard contents into the search area of the newly selected tab. This is very cumbersome and makes Kate almost unusable for searching. Bear in mind that this must be performed for each tab that you have open and that it is a real pain... Solution: Allow the current search context to be retained regardless of which tab is selected. In this case, clicking on a tab and then pressing F3 (continued search) finds all subsequent occurrences of the current search string without having to open a new search bar. The way I am suggesting is standard functionality for most other advanced editors.
Thanks for the report. Please try the search plugin that is designed for searching in multiple files.
I will try the plugin as a workaround but I'm not sure that is a solution to the fundamental problem that for such a first class editor, basic search functions are missing. If there is a such a plugin then as you have already suggested in another report it might be wise to incorporate its functions into the core of Kate. Kate is such a good editor in most respects but with regard to search it feels rather second-rate. It does need to be fixed.
The search plugin should have been enabled by default, but the shortcuts are not set by default. I myself have changed the shortcuts and would be happy if the that would be the default for kate :) You change the shortcuts in Settings-> Configure Shortcuts... Then search for "Search in Files" and re-assign Ctrl-F to it. You can also reassign F3 to "Go to Next Match" and Shift+F3 to "Go to Previous Match" I actually find the Search plugin to be superior to the one in Notepad++, but I guess I might be a bit biased ;)