Thanks for answering my questions.

It is possible that there has been some loss of muscle mass under/around the eye, which causes the third eyelid to be more prominant. This is actually pretty common in older dogs and in the absence of any sort of injury or trauma noted, I'd tend to think that's what is going on with your dog.

That being said, it may not be a bad idea to ask your vet for a referral to a veterinary eye specialist. These are the vets who deal exclusively in problems in/around the eye and may have a better idea of what is causing this problem with the third eyelid (also called the nictating membrane).

It's also possible that the eye drops that they sent out simply weren't enough to get the job done, so you may want to ask the vet if they want to try sending out something different. Unfortunately when it comes to eyes, sometimes you have to try different medications before you find the one to do the trick.

I hope this helps.