Can multiple facelifts damage the underlying skin enough to cause permanent rippling?

I'm sorry to hear about your concern. Multiple facelifts can,
indeed, add to "rippling" of the skin. If it occurs, it is usually
due to scar tissue or sutures that are placed. Fillers (including fat transfer)
can help to camouflage the rippling. Occasionally more surgery is needed. If
the rippling is due to scar tissue, it may resolve over time as the scars
mature and the skin contracts. Best wishes.

Rippling of the skin after facelift suture can be due to many factors, such as blood clot, swelling, scar tissue, stitches, folding of tissue, etc. Most irregularities after facelift are temporary. Keep in mind that scar tissue occurs after each surgery, and repeated surgery of the face or neck can contribute to permanent rippling. Multiple facelift procedures may contribute to permanent rippling of the skin. Treatment is variable. Filler or fat injections is a good option to consider.Best,Dr. Chaboki

If you have some lumpiness or rippling in your face after having had three facelifts by the age of 59, I think an argument can be made that more surgery is not the answer.  Using fillers to correct some of this should work.  Also, strategic use of fat grafts might have some application, but I do think that a hands off policy at this point might  make the most sense.Dr. Hargrave 

The combination of aging and multiple facelifts certainly can impact the condition of your skin.  Your seeking out a cosmetic dermatologist is a good idea.  Sometimes, laser resurfacing can be helpful, as well.  Unfortunately, without photos it is difficult to provide more precise advice.