A few thoughts. I agree that starting a new exercise plan can result in water retention so you can pounds on the scale that aren't real pounds.
You indicate you are 5'4" and weigh 180 pounds. I am also 5'4" and weigh about a pound more than that.
How much you can lose eating 1500 calories a day really does depend on your activity level. Do you know what your basal metabolic rate is? There are a variety of calculators out there. Most of them are based upon your age and weight. I find those seem to overestimate my calorie burn.
If you know your body fat percentage, I like the Katch McArdle calculator:
http://www.calculatorpro.com/calcula...mr-calculator/
(If you don't know body fat percentage you can estimate it using measurements:
http://www.scientificpsychic.com/fitness/diet.html)
For me, my BMR using the formula is about 1350 calories a day. That is just BMR if I was laying around all day. I wear a Fitbit so I know that how many calories I burn beyond that is highly dependent on activity.
Now, Fitbit using a BMR calculator that is more generous than the one above, by about 100 calories (that is, it puts my BMR somewhere around 1450 calories roughly). On days that I don't leave the house (not uncommon since I work from home) if I am on the computer a lot I may burn according to Fitbit only around 1600 calories and I really think that is over stating it by about 100 so really close to 1500 calories. If I'm eating 1500 calories then I won't lose weight.
Of course, I don't always sit around the house. I did a long walk the other day in the neighborhood (over an hour long). It is a hilly neighborhood so Fitbit counted almost all of it was very active minutes. I also did some weight lifting. According to Fitbit I burned just over 1900 calories (again, I think it was probably closer to 1800 calories).
Now, we all vary as to activity. Someone who has a job where they move around a lot more burns a lot more calories for example. But, depending on your lifestyle kickboxing a few times a week may not add a lot of calories to your daily activity.
So - I do think your lack of a loss may be temporary due to water retention.
But, if you continue to not show a loss than you don't have a calorie deficit. In that case, you may not be burning as many calories as you think. Another possibility is that you are eating more than 1500 calories a day. I also count calories and am also really careful in doing it. However, I sometimes eat out and I'm not at all sure that restaurants are all that careful that what they make matches up with the calorie counts that restaurants may show. So, even if you are really careful, if you eat out much, it doesn't take a lot of mistakes by restaurants to put you over on calories.