Yes.
Absolutely!
Littles should care just as much for their Caregiver as they receive care from them.
Perhaps the care is shown in a different way though, and perhaps sometimes they have to make personal sacrifices to make sure their partner is happy too. This is why you should get to know your partner well before you enter a relationship with them. If you don't know their methods of showing care then maybe sometimes you don't know when they're trying to show you that care.
For me, past partners have shown me care when I've been feeling down by doing things that uplift me. They have colored pictures for me, made little artwork or crafts, or have given me some sort of authority by asking me for direction about very small tasks (sometimes just given the opportunity to be in charge when you feel out of control in another area feels great).
Some have gotten bandaids for ouchies, given me kisses for said ouchies, or have held me in comfort when I cried.
Littles are very well capable of hugging, kisses, giving apologies, and having adult conversation.
I think it is easy for them to forget that, while they play into being a cute 3-year-old, they are still an adult and are capable of acting as such or communicating as such. Sometimes showing love and care is talking about a serious subject with your partner so that they can get all of their thoughts and feelings out there and understood by somebody that means something to them.
If a little is not willing to care for their Caregiver then I feel like they aren't really devoted to that relationship. It could be that they're very young and inexperienced with relationships though. It could be that they're just generally selfish and have the wrong impression of the Caregiver/little relationship. There could be many factors to their lack of effort.
We are more than just Caregivers. We are more than just these relationship dynamics. We are people. We have feelings and needs too.
Just because I identify as someone who enjoys providing care for another person doesn't mean I never expect to also be cared for or given to by my partner. I believe that healthy relationships are balanced with important aspects such as feeling cared for by each other.
I wouldn't typically drop someone (assuming that I felt the person was decently experienced with relationships) instantly because I felt like they failed at showing care for me in a moment that I needed, but I would have a heart to heart talk with them to bring it to their attention. If I felt like then my needs were still being neglected then, yes, it's proven to me that whoever that person is just isn't the person for me.
Littles can care and should care.