It used to be that whenever I was dating someone and I thought they'd rather be spending time with someone else I would back off and not ask for any of their time. I didn't want to feel like I was competing and I didn't want to be interfering in their chance for maximum joy.
This was a wrong choice, not just because it was self-defeating and resulted in me missing out on my best chances to be close with some of my favorite people, but because I was essentially trying to make someone else's choices for them. It's not my job to predict how much of me someone else wants in their life, and I should be relying on them to tell me that, not trying to guess it based on my own observations. Also, someone might appear to be happier about something else, or even actually be happier about something else, without that meaning that happiness about me is invalid or not valuable.
So in the future I am going to resist this urge as much as possible, and if I feel like I am being put into a competitive situation or used as a consolation prize, then I will discuss that with the person. Or if I feel like we have different levels of desire for each other's company then I will ask them to define what they want from me.
Whatever the case, I will not allow my impulse to back off to be my first response to feeling like my time is not valued or desired. First I will ask questions.