Quite often, when exploring the tested application (especially - the web one), one would set some filter for the Object Browser (Search field in the top-right corner) and then navigate through several objects in order to check if the filtered property/method is supported by the selected object and what value does it have.
Currently this is not possible, because the filter field is cleared when another object is selected in the Objects tree. This forces user to either scroll the list of properties/methods and look for the required property/method, or to re-enter the filter value. This is inconvenient.
Enhancement request: Keep the filter active until it is cleared explicitly by the user. Considering small size of the Clear button for the filter, it would be handy if it keeps the focus after the new object is selected in the Object Browser so that user can clear the filter by pressing Esc (exactly as this is possible now).