I have noticed he has forgotten things before--not this important. Is this typical of BPD? How do I handle it? It doesn't seem malicious but becomes annoying.
I wouldn't say this type of forgetting is part of BPD.
You ask how to handle situations like this? I would say when it is important, like taking care of your dog, you should make other arrangements. He is not dependable in that area. You can also write things down for him depending on what the task is.
What other examples do you have? Is there a pattern you can see?
