Over watering is the biggest cause for plants death. A good indication is 'chlorosis' that makes leaves turn yellow and drop off. Self watering pots might be fine for flower baskets and things that are difficult to keep well watered, but most herbs do not like to be soaking wet all the time. OLder laves will turn yellow and die out naturally as well. This same extact question was just asked here in a very recent thread.

Thank you for your answer. The potting mix is staying moist all of the time. I have a very large Peace Lily in a regular container and the bottom leaves constantly turn yellow and die, which I thought was from lack of light.

Again, way too much watering! I have a large pot for a small fig tree and its leaves droop after just two days without water. Its in a huge pot 20"x20"x20" and still can take in almost a gallon or water every other day. I do check it daily and only water when the leaves start to droop a little.