The half-life of Estradiol in your blood system after a patch is removed is just under 3 hours. This means that in about 14 hours (5 half-lives) after the patch is gone, your Estradiol levels are almost zero.
Patches are very good at keeping your blood levels constant as the medication is slowly released into your blood system constantly as long as the patch is in contact with your skin. When the patch comes off, you no longer have any Estradiol going into your body, but it is still being eliminated by your liver and kidneys, giving you the 3 hour half-life.
Libido is too complicated of an issue to use it as an indicator of your Estradiol levels. If you experienced any increase in libido it may or may not be related to a lost patch. Just check to see if it is still there. You should be changing these patches twice a week anyway.