If you can find someone who can pressure test your entire cooling system and cap that would be best.. You may have a loose hose or connection somewhere that is not holding pressure. THey have a little hand pump and gage setup that attaches in place of the cap , using the right adaptor, that applies 4-10 lbs or so, then you look for pressure dropping and obvious leaks.
The cap is tested the same way. It might take some searching to find someone with the correct adapter to pressure check it, depending on which radiator and cap your jeep has.
Or, just buy the new cap and see if it cures it.