Yes, you definitively can be losing
fat at the same time you're not losing weight on the scales. That's because scales measure everything in your body: skin, bone, muscle, hair, blood, fat and
water. And water is often the reason that fat loss doesn't show up on the scales right away.
An obesity researcher explained it this way to me - often when a fat cell empties out, it temporarily fills up with water. The fat is gone - yay! - but you can't tell on the scales because of the water. Then sometimes we have a big water whoosh and the scale drops down a couple of pounds overnight. We didn't lose that much fat overnight of course - it's just that the water finally left the fat cells.
It happens to me a lot - if I seem to spend a day running to the bathroom (or especially overnight), then I'll see a loss the next morning when I weigh myself.
So the thing to remember is that you're
always losing fat when you create a calorie deficit through exercise and planned eating, but it might take a little time to show up on the scales. Just like you said, your body is still getting thinner and healthier, even if it doesn't show up right away. Everyone hits plateaus once in a while! Just don't let it play a mind game on you.