If a girl is losing interest, it would work in your favor to try having a different kind of conversation with her.
Introduce flirtation into your conversations and tease her.
This may be what she has been waiting for and you have yet to deliver on it.
Flirtation and teasing are often very effective in getting a girl to feel more engaged with a guy that she is talking to.
It lets her know that the guy is interested and it also makes her feel as though the both of you are connecting on a more intimate level.
So, yes, it is best to act and initiate these kinds of conversations as opposed to merely backing off and acting as if you have lost interest as well.
If you were to act as though you have lost interest in her as well, you could end up losing her interest entirely because she would feel as though you didn’t value the relationship enough to try to save it or keep it going.