The league search function opens as a popup, allowing you to enter text to search, e.g. 'World'. When you get the results, clicking takes you to that league and closes the tab. You can't go 'back' to the results, and you can't 'right click' to open them in a new tab or something, so the results are lost each time. When you do a seach again, because it is string-based and fairly arbitrary, the results can be quite different, so you can't simply go back to where you were.
Since the search results list doesn't really provide enough information to see if the league is good, you do need to open it to see if it's active.
(Minor rant: even that's annoying as you can't just go by posts, the best option is to open recent races to see how many cars finished on the last lap - and then this is impossible if the league is on its season break because you can't see the previous seasons results.)
Suggestion: either clicking on a result opens it in a new browser tab or the search does not open a popup but is a switchable tab (like Race/Setup/Strategy on the race strategy setup page) and results can be right-clicked.
However, having said all of the above, a much better idea in my opinion would be a little bit of a revamp of the filters:
-remove the search popup, integrate it into the filters.
-allow the time filter to be ignored (because you may be looking for a league but not know what time it starts).