Almost everyone reaches a plateau at some point in their weight loss program. The reason is that the human body works hard to keep energy intake and output in balance. 
Plateaus happen simply because our bodies will adapt to any exercise program over time.  This is usually the time when we lose motivation to stick to a new healthy way of living.

Reasons for and solutions to weight loss plateaus:

Lowering your energy intake too much

When you decrease your food intake, your body simply lowers its metabolic rate in response. This still allows the body to function properly, but ultimately your body requires less energy which prevents you from losing more weight.

Keep your kilojoules slightly below your maintenance kilojoules so that your energy levels and metabolism remain high. 

Loss of lean body mass

Lean muscle uses five times the energy as fat mass.  If you lose muscle, your metabolism drops and your weight loss stops.  Since the body finds it easier to turn muscle into energy than to burn stored body fat, being on strict energy restricted diet will lead to muscle loss.

Make sure your exercise program is combined with a diet that creates a safe energy deficit along with enough protein and nutrients to prevent any deficiencies. Exercise increases lean body mass, which in turn increase metabolism.

Weight loss

When you weigh less, it takes less energy to move your body and therefore a weight loss will lead to a reduced energy requirement.

Make sure you follow a weight training program to help increase lean body mass, which can help compensate for the loss of energy.

The 'Adaptation' Phase ends

When starting a new exercise program, your body responds because it is required to make numerous changes to adjust to different workloads. Your muscles are rebuilding themselves and this uses a lot of energy. But, at some point your body will stop adapting to the new workload and, as a result, you will burn less energy for the same activities.

Don't let your body get used to the exercise. The key to avoiding plateaus is to change your strength training and cardiovascular workouts every 4-6 weeks.

Exercise efficiency

The more you do something, the better your body becomes at performing the exercises and can actually use less energy during the exercise.

Concentrate on more dramatic changes such as trying brand new activities. Change the intensity, duration, frequency and/or the mode of exercise if necessary.

Over-training

Just like not eating enough can lower the amount of energy you burn, so can over-training. When you exercise too much, there is a point of diminishing returns when an increase in exercise energy expenditure is negated by an equal decrease in non-exercise energy expenditure. In other words, when you increase your exercise intensity, your body responds by decreasing the amount of kilojoules you burn during the rest of your day.

Take time to recover. If you reach exercise burnout, this is a great time to take a break for a few days, or try something gentle like yoga or a stretching routine

Enhanced physical condition

As you get into better shape, your body is more efficient and it uses less energy to operate. Improved health means a lower resting metabolic rate and less energy is burned during normal daily activities. Part of this is because your cardio-pulmonary system is more efficient now and you have a lower resting heart rate.

At this stage you are officially in shape and healthy.  Focus on that and feel good about yourself.