I'm not sure if it helps, but as an aspie woman I get all of the below at times. Although I likely have ADHD too, so unless I am very compatible with whoever I'm around then I tend to need time to 'regroup' and focus on other things for a while.
"My Aspie boyfriend often talks about getting bored of people. We are on a break right now because he seems to get bored with me. He says he adores me, but over the last month or so he doesn't seem as attentive and he doesn't engage in texting so much anymore. I honestly think he likes the excitement of finding out about people through new relationships and then when the excitement wears off, it feels like he needs something more exciting."
What is your personality like? I can be quite serious and 'academic' at work or when required, but the rest of me is very hyperactive, creative and often immature and I need this combination in a partner too. Are you a good match in this sense? Or could you learn to be more exciting (by his standards)? I don't mean you have to constantly entertain him, but just doing the odd random thing that gets his attention? Also, how much do you flirt with him? I've noticed a lot of women have a tendancy to flirt with their partner in order to get into a relationship, then for some reason stop doing this once they've got the man they want. I don't know if this applies in your case, but it's a general observation.
"What is odd is he doesn't want to go out in public too much. He gets overwhelmed with too much stimulation and gets plenty of that with his demanding job. We have had dinners and breakfasts together often."
I have periods of time where I am insanely busy for a few weeks working on a project and don't have the energy to face socialising afterwards. I'm not sure if that is specifically an aspie trait or a workaholic one, but if he is still making an effort to keep in contact with you then I wouldn't worry on that point. For me, 'stimulation' can be positive or negative. I could be utterly exhausted by work, but still respond positively to certain behaviour from my partner.
"He also prefers texting over talking on the phone and things can't be discussed easily over text messaging so it is almost impossible to have a decent relationship anyway."
For you. If he is anything like me, then writing things down and having time to think and edit responses rather than try to form coherent sentences immediately is MUCH easier than discussing things over the phone. My brain to mouth connection is pretty dire at times and I tend to be overly blunt, inappropriate or just plain weird when I talk. Fortunately, I inherited a posh accent and most people find it amusing, but writing/texting allows me to slow down and better structure my thoughts. If you want my honest, considered opinion on something, then texting is far better than a phone conversation. Face to face is also better than a phone call, as at least I can get added context from facial expressions or gestures.
"I am starting to think he needs new excitement all the time and that's perhaps just the way it is."
Possibly, but that doesn't neccessarily mean a new partner. With the right person, I can be constantly entertained and he may feel the same way.