Get a Heart Rate monitor, if you have one in the elliptical trainer use it correctly.
Use a formula to get your correct Heart Rate so you exercise in the fat burning zone. You sound like you are going way too fast and you are draining yourself, not burning calories. Too vigorous exercise might burn your muscles and not the stored fat. If you are doing only 3 minutes at the time, you are definitely going WAY too fast. Slow down and do a continuous 20 minutes workout at a lesser phase. The starting fat burning zone might be too slow at first (maybe frustratingly slow) but that is the way to SLOWLY build resistance. The longer you exercise, the slower your heart rate will become so your efforts change (you create more resistance).
You can alternate, slow one day, and intervals of fast and slow the next day.
If you do cardio for weight loss you MUST pay attention to your heart rate to see results. That is what is working for me.
http://www.polarusa.com/consumer/fitness/hrm.asp The formula here is for both men and woman.