I can't tell if they can be saved without pictures (and possibly not even then). One of the things that could have happened to them is root rot. So you need to slide the root ball out of the pot it is in. Check to see if it is pot bound (i.e. roots going around the outside of the ball in circles). Then gently wash some of the soil off and check the roots. They should be light colored and firm. If they are brown/black, mushy, or smell bad, they are rotted. If there are some that are healthy, prune out all the rotten ones. Loosen any that have been going around the outside, so that all the roots are hanging down. Then repot in potting soil made for cactus/succulents which will be much less moisture retentive.
Thyme is a desert plant. You have been killing it with kindness. Watering daily is way too much (if you have been wetting it thoroughly each time). What you want to do is water it until all the soil is moistened and water is running out the drain holes. Let it drain and then DON"T WATER AGAIN until the top couple inches of the soil are dry. Depending on your soil type, how much sun it gets, etc., that might be once a week or it might be every other week. I have had house plants I watered once a month.