Out of sight, somewhat out of mind. There are a few things to understand about this. Firstly, it isn't out of intentional rudeness or lack of care. Secondly, at least in my case, I find it annoying when people try to 'keep in touch' with me (more about this below). I, and I suspect many others here as well, are kind of stuck in the present moment. We experience each moment vividly, and if anything we don't want to experience at the moment (such as an anxious call from a loved one) arises, we don't deal with it if possible. Thirdly, from my own observations, it seems people with AS think about people much less in our alone time than NTs do, though people are still important to us.
When I was 19, my grandmother tried frantically to contact me. She didn't know where I was or if I was OK, and she hadn't heard from me in months. Now this might seem strange to you, but every time she called where I was staying at, I got really annoyed. I didn't feel like being all emotional with her, especially over the phone. And I don't really enjoy speaking to people that aren't physically present. So I ignored some of her calls, and as she started calling more I realized the situation was becoming compounded (her emotions were building up further), so eventually I took one of her calls to get her to stop calling so much. I guess my behavior hurt her feelings a lot, and she even cried over the phone. Whenever she expressed that I was hurting her feelings, she was only bothering me more, even angering me. She said she didn't understand how I could be so cold, but I thought I was acting normal. What I felt I needed was distance, because to me it doesn't make any sense to talk to someone over the phone unless it's about either an important matter or for making plans. What my grandmother wanted was to be emotional with me, which I'm generally not comfortable with unless I really trust the other person. Trust is a very difficult point for me to reach with someone given how much I've been hurt in the past; it is a level of communication that I share with no one at this time, but even with trusted ones I really prefer to be with them in person rather than over the phone.