Jason, I know exactly what you are talking about. I sometimes lose what the conversation is about, or foget names of people who I really am good friends with. I sometimes tell a joke and half way through get it back to front, or forget half of it!
It is the same as you are experiencing, it is generally when under stress when it occurs. Try to find less stressful ways of doing the job, and be more organised if it is possible.
Give yourself relaxation time when at home, to ease the tension of the day, paricularly before going to bed, even if it is only for a half hour.
Another tip is, don't rush about during the day, be calm and curteous when driving. It is amazing if you take a look on your life, and see the things that can add to the stress. Identify them, and cut them out, one by one.
If I drive, I take it easy, and just relax, may take me a couple of minutes more of my time, but I get home a little more relaxed than otherwise.
Don't know if it is DID, that causes these problems, but I guess it is.
All I know is, that it will get easier in time or rather, people will get to know you and accept it, they do with me, even though I get teased I have a quick wit, which usually suffices.
I do know how hard this can be, I hope you can get to handle it,
ste