How Common Are Long-Term Effects of Blepharoplasty - Especially Sunken Eyes?

So much depends on your actual anatomic details.  As indicated by Dr. Cohen, over done surgery does cause a rash of issues.  Being conservative with surgery or avoiding surgery altogether prevents a lot of the complications associated with eyelid surgery.  It is important to understand that there are several types of surgeons who offer cosmetic eyelid surgery: general plastic surgeons, facial plastic surgeons, and oculoplastic surgeons.  Without a doubt oculoplastic surgeons have the most specialized training in eyelid surgery.  This is important for a 53 year old who is considering eyelid surgery.  The reason being is that at this age, all blepharoplasty involve a degree of reconstructive considerations.  This is no place to let someone who is not subspecialty trained in eyelid surgery to dabble.  The American  Society for Ophthalmic Plastic and Reconstructive Surgery maintains a website with a directory that can help you find a well qualified eyelid surgeon: ASOPRS.org

Current techniques are appropriately more conservative regarding fat removal as hollow, sunken eyes are a sign of advanced age.  In fact, you can ask your surgeon directly how much fat he intends to remove to get an idea of how aggressive his technique may be.  I have, at times, recommended adding fat by micro-transfers to bring back the fat of youthful eyelids with nice results.

Lower lid blepharoplasty should ideally preserve most or all of a patient’s lower lid fat, unless there truly is marked excess that is bulging outward. Fat can not only be treated by removal – it can also be restrained, and it can even be repositioned into areas of hollowness such as the tear trough. In addition, fat can be added to areas of hollowness in and around the lower lids to camouflage or ‘correct’ adjacent areas of fullness. I frequently perform structural fat grafting of the lower lid / cheek junction at the time of lower blepharoplasty, to add lower lid support and to blend the contour of the lid and cheek.
Fat grafting of the lower lid area requires experience and meticulous technique. As the area is covered by a very thin layer of skin and muscle, overcorrection must be absolutely avoided. My approach is to graft fat to the point that the area looks aesthetically ideal, then stop and wait 3 months to assess fat survival. As fat survival is variable, additional fat grafting procedures may be performed based on the results of the first. In most cases of post-surgical lower lid hollowness, two to three fat grafting procedures are required to restore adequate subcutaneous fullness in this area. 

During the blepharoplasty procedure only a conservative amount of fat should be removed or else a sunken eyed appearance will result. It is important not to take too much skin out of the upper lids so that you can close your eyelids and not to have scleral show. Make sure your surgeon has performed thousands of blepharoplasty and eyelid surgeries.  

Sunken eyes can happen if patients are prone and they had over resection of fat in the lower lid.  Hard to say for you without an evaluation.