we cannot be expected to continue paying our affiliates for old business if the affiliate has not actively promoted our brand or referred a single customer for a significant period of time.
Wrong. What does the continued promotion of your business have to do with regular customers that were referred by an affiliate months ago? I'll answer for you ... nothing. It is not like existing customers are going to stop wagering with you because an affiliate site changes a few banners or pages around.
There are many programs in this industry that advertise and pay a commission FOR LIFE of the player. So yes you can and in fact are expected to pay for "old business" because if it wasn't for the affiliate referring them to you, you would not have had the player in the first place.
I was another of the many affiliates who were not emailed when you dropped the old program and replaced it, contrary to your statements above. Thankfully we have never (and probably will never after reading your post) sent you much business.
I highly encourage you to submit your program for certification here. You might be surprised at the result.