Yes, in my experience both depression and anxiety can effect memory. And for sure if you are AD then remembering things is an extra challenge. I depend on lists to remind me of things I need to do and I also use them to motivate me to do something when I am in avoidance mode (like now).

Anxiety can even cause you to forget obvious things. I sometimes can't even remember my own son's name. When he was a baby I would just call him 'junior' because I couldn't remember his name. He is 16 and still there are times when I have to think hard to remember his name. I am hopeless with work clients and have to play lots of mind tricks to try to remember names of people I have been working with for years and years.

Keep a list for those tasks that skip your memory and then you won't have to try to remember.