It seems to me, DJCT, that the problem here isn't exactly what you think it is.
I really think that she feels you're taken her for granted and/or not really loving her. I'm going to explain a concept here for you and I'd like you to try it out and see if it helps any, as I do think it will.
People have different ways of communicating love. It has to do with the way they were brought up, their role models, their own preferences and the influences in their lives.
So, when they want to show their love to someone, they act in that particular way. And, conversely, when they're treated in that same way, they in turn, feel loved. Makes sense so far?
Primarily, there are five different ways that people express love. They verbalize it with compliments, encouragement and praises, or they physically demonstrate it with hugs, caresses and touches, or they like to give little gifts as treasures of their love, or they like to do errands and chores for their loved one, and some simply enjoy quality time and conversation with their lovers.
"She is often sweet. Cooks for me, rubs my back, buys me little presents here and there"
So your woman seems to express her love to you by performing some chores for you, and with acts of physical touch and giving little gifts.
When she asked you to run a chore for her... you saw it as making you into a chump, doing her a ridiculous favor.
But she doesn't see it that way. To her, it's an expression of your love back to her. It's one of the ways she expresses love, so it means "love" to her. Get it?
It's not unusual for two people to not see the same things as meaning "love". As I mentioned above, it has to do with our own preferences, our role models growing up, other influences, etc. To you, it seems you feel more loved when a woman has sexual relations with you. Lots of guys feel that way. Maybe you feel you're communicating your love when you're having sex with your lover. So to you, running an errand or buying her a silly little inexpensive surprise gift seems AFCish.
So I'd strongly suggest you do a few little chores for her and try this experiment out. Next time you're at the store, for example, call her and ask her if she needs anything. Also, take care of a chore around the house once in a while that she normally does, and don't even tell her that you're going to do it, just do it. Once every month or so, on a different day to keep it unpredictable, pick up a little inexpensive something for her while you're out: a funny card, a large cookie, something silly that reminded you of her, and surprise her with it. Give her a massage one night without going for sex, give her a warm little rub on the back when you pass her in the hallway.
We're just covering all the different ways she expresses love with you doing the same back to her, and watch to see which get the biggest reactions from her. This may sound silly or chumpish to you, but try it. You'd be surprised what her reaction will be like. Relationship require maintenance.
This is why she doesn't think you're being "romantic". You're not demonstrating love to her in a way that means something to her. You're not "speaking" her romantic lingo. And this is why she's feeling that you only are using her for sex, because she feels neglected and unloved. If she continues to feel that way, she'll dump you eventually.
Which answers your original question: I'm guessing this neglect is a major reason why your LTRs went south.