How accurate are these calorie counters?

Generally calorie calculators are wrong.  They're estimates only, same with the basal metabolic rates.  The food caloric data is from the USDA usually.  I think that data is pretty old now and things have changed a bit.  How did you determine your portion sizes?

Based on what you're describing, either the estimates were pretty decent and your body has lowered it's metabolism to handle such a deficit or your body composition has changed leaving your weight the same.  I'd recommend using body measurements to track your diet instead.  You can get a decent cloth tape measure in the sewing department and use it to track changes to waist line, arm, thigh and a few other points.  Adjust your diet to keep those moving in the right direction.

This is where I am please with the Calorie King software that I use. Last month the Calorie King software predicted my weight-loss at 15lbs and I actually recorded a weight-loss of 19lbs. I know that this software is leading me toward my goals each week/month.

Like so many things, I think the weight gain/loss = calorie surplus/deficit equation only works in moderation.  Past a certain threshold and other factors come into play.  On the other end of the spectrum, your body can only absorb so much food in a day.  So if I eat perfect 6 days a week and then 10,000 calories in one day, I haven't ruined my week.  Eating that much may cause other issues a couple days done the road, but I could still lose waiting doing that.  And in fact I did lose weight doing that.  For almost two years my wife and I journaled our food intake and lost a combined 160 pounds.  Six days of good eating, one day of being bad.  And some weeks, we were really, really bad.  We would safe up our cravings throughout the week and then just went nuts on our day off.

I'm not an expert by any stretch, but I do know from personal experience that eating too little can be an issue.  As I got down closer to my goal weight, losing weight became more difficult.  I also noticed energy levels dipping and recovery times lengthening.  I had to increase my calorie intake (specifically protein) from 2000 to 2500/day.  I had more energy, which allowed me to workout harder, keep my metabalism up, build muscle, and slowly drop the extra weight.  I eventually got down to a 9.8% BF.  I haven't sustained that (this was back in 2004), but even today I can still claim an almost 100 pound weight loss by doing the six day on, one day off strategy.