NT/AS Clue: If you want something done right away, just do it yourself! If you want something done right, ask your aspie to do it.
One of my NT expectations that I have had to let go is wanting things done quickly by my aspie spouse. Whether it be answering a question, taking out the garbage, or even chasing the toddler before he runs into the street, you must drop the expectation for the aspie to respond quickly. He probably cannot do it. In his mind, he may think he's responding quickly enough. But it's likely that he is not. So stop expecting him to respond quickly. Definitely stop demanding that he respond quickly. Make it your goal to be okay with the fact that this is something he simply cannot do.
If you want something done right away, just do it yourself. Granted, this is difficult when you have the flu and you've asked for a drink of water. You may need to hire some help or beg friends/family to come by if you're really ill or recovering from surgery. But if your very first instinct when you want something done immediately or even quickly can become to do it yourself, you will be a much happier person in an NT/AS relationship.
Now, don't give up asking him to help altogether. If you want something done right, in many cases (at least in my relationship), it's best to ask your aspie to do it. He will devote much time (hours, days, possibly weeks) to performing the task with excellence. He will pay attention to detail and the job will be done, often to perfection. My husband will follow the pattern of the hardwoods when cleaning the floors, so corners I never hit will be cleaned well! This kind of attention to detail and dedication to excellence takes time. So don't ask for his help if you're not willing for it to take (sometimes a lot) of time.