Column search and/or filter settings are not saved if you have clicked through to a Timeline page and then click the browser Back button to return to the list page, at least not by the system.
Some browsers, in particular WebKit-based browsers, such as Google Chrome and Safari, do try to remember your settings though, but this doesn't quite always work (known issue with WebKit itself).
Unexpected and unintended list filtering behaviour may therefore be noticed when you use the browser Back button. e.g. A search term from one column may end up being copied to a different column.
Just use the standard browser function to open Timeline pages in new tabs or windows if you want click through to Timeline page from a filtered list and maintain your filter settings.
i.e. Either right click on Timeline links and chose the appropriate option (see below screenshot) or hold down Ctrl (new tab) or Shift (new window) when clicking them.
You can then just close down the additional tabs/windows when you're done and return to your original tab/window which will still have your original filtered list.