I know how this is...but please do not give up. You are worth it to be healthy for yourself. Slow weight loss is still loss. Don't do the starvation business. We all know where that leads. Although I have never tried South Beach diet, I have tried many and the only thing that has worked for me is calorie counting and lots of physical activity. I should add that dedication to doing it every single day has been the most important component of losing the weight this time.
I don't give myself any excuses whatsoever. I don't care what hubby or kids are eating. I am doing this and that's all there is to it. I go to the gym at least 6 days out of 7, no matter what is going on around me. No excuses. I decided to give this one full year of my full attention and see where I was in a year. I truly didn't care if I lost 10, 20, 50 or 100 lbs. I was going to stick to my plan like glue for one full year. It will be 10 months on April 15th, and I have already lost 92 lbs.

You can do this! Don't get down on yourself and please don't see a small weight loss as a failure, because it isn't. It's a victory. If you lose 2 lbs. every 2 weeks for a year, you will have lost 52 lbs. in a year. Nothing failure-like about that!
Good luck to you! You can do this!