...You will find every instructor in any discipline will ask you to put your heels down. It may not have seemed to matter when you first learned, but it's been realized its important now...
Gotta disagree. Particularly during the first half dozen lessons, heels down is horrible advice. When starting out, it almost always - at least with older students - results in using the leg to shove the heel down, causing tension in the leg. Tense legs bracing against the stirrups = horrible riding.
Heels down depends on the flexibility of the student combined with where the heel is in relation to the hip. Older students won't have a ton of flexibility, and it will take months or years to improve it. Furthermore, if the instructor is also teaching heel under hip, then it is almost impossible for many people to put the heel down.
Sitting in your chair, slide your heel under your hip. Now raise your toe. I'm 54, I've been riding for 4 years, and I cannot raise my toe in that position. Nor does it help if I partially stand and imitate the degree of knee bend when riding. Now move your heel 6 inches forward and try again. At that point, I can raise my toes a couple of inches.
So for those of us not born in the saddle, how much you can raise your toe (and thus how much heel down you body is physically capable of accepting) is related to heel-hip alignment - and too many instructors stress heel under hip. That is another marginal piece of advice, depending on what kind of riding you are doing.
If I were the OP, I'd look for another instructor. Maybe go back to western. Western riders don't stress over "shoulder-hip-heel vertically aligned" or "toes forward" or "heels down". With time, the OP will be able to more closely align shoulder-hip-heel, and maybe even figure out when that is useful and when it is not. "Heels down" will come with time, and with time you MIGHT be able to do it with your heel under your hip - although I still cannot after 4 years of riding.
But the big problem, IMHO, is that most instructors learned to ride as kids, when their bodies were wet noodles waiting to be shaped. That doesn't work for squat when you learn past 20 maybe, and certainly not when 40+. The point of good riding is to feel your horse's motion and learn to move in synch with your horse, and to do so in a position that allows you enough stability and control not to hit the dirt - another things that hurts more when older!
If the OP wants to continue riding sort of English, then I recommend an Australian saddle. It will place you in a mild chair seat, which makes it easier to get the heels down. Most feel very much like an English saddle. I can switch in one ride between my Bates Caprilli and my DownUnder Master Campdraft, and with my eyes shut it would be hard to tell the difference. It also is more secure if the horse hits the fan:
If your goal is dressage or jumping, stay English. If you want to relax and have fun riding horses, I'd switch to western for at least a year or so. I find the English riding approach to using the reins irritating and a lot of the instruction given in it sets you up for jumping or dressage rather than just having fun. But mostly, I'd at least talk with your instructor about learning as an older student. Some instructors don't take that well, in which case I'd find someone else. I might do it anyway, because I think you are getting bad instruction.
PS - my tag line comes from a well known ENGLISH-style riding instructor...
PSS - An amazing collection of pictures of cowboys from around 1905-1915 can be found here: http://www.cartermuseum.org/collecti...ion.php?mcat=3