Doilies really aren't that hard to care for, especially if you know what not to do with them.
I have made, sold, and decorated with a lot of doilies over the years. I've always recommended to my customers the same care plan that I have used myself with much success at keeping my doilies looking beautiful for many years.
Washing: To keep my doilies looking their best, I prefer to hand wash them. Suds up a little bit of dish soap or mild detergent in a sink of lukewarm water. Don't overdo the soap, it doesn't take much. You just need a bit of suds, not a lot. Soak the doily for a bit, swishing a few times, then drain and fill the sink with plain water for rinsing. Swish the doily in the rinse water; drain and repeat until no suds are left. Gently squeeze the doily to remove most of the water, being careful not to wring it. Press the doily between two layers of a thick towel to absorb the remaining water. Smooth the doily into shape on the top layer of the towel and leave to dry. Important: Most doilies are 100% cotton. Do not wash your doily in hot water, and do not dry your doily in the dryer, as your doily will shrink and be ruined. (I have heard too many horror stories.)
Repairs: I have never needed to repair any of my own handmade doilies, but I have repaired quite a few vintage and antique doilies for others. For those of you that do have doilies in need of repair work, I will try to write a how-to repair article for another post in the future. Or you might want to look for someone who does quality crochet work and see if they can do the repair work for you.