I don't think the oring in the cap is so much to prevent air leaking out (although it may help with that) as to prevent water and crud from getting in to the top of the schrader valve.
If the tire is losing air faster then normal, then check to make sure the schrader valve is fully seated with a schrader valve wrench. You can check that the schrader valve is not leaking with a bit of liquid soap (or just common spit!!). If still leaking, then replace it.
Other leaks are more likely: nails, screws, glass bits, or other sharps that have penetrated through the tread into the tire.
Lastly if the tire has been replaced recently and is leaking air, then the bead may not be fully seated on the rim. This should be corrected immediately with as little riding as possible until done especially if it is the front tire.
Cheers,
TQ