Arms do lose their firmness. This could be due to triceps atrophy or the loss of tone and size from lack of exercise, which could also cause excess subcutaneous fat in the arms and body.
The lack of firmness in the posterior is commonly due to two factors. Firstly, the buttock (gluteal) muscles may atrophy or, secondly, it may be the result of excess body fat. Poor nutrition or a lack of adequate exercise are the usual suspects which lead to this.
This fat is sandwiched between the gluteal muscles and the skin. Ultimately, exercising and strengthening the gluteal muscles will aid in the loss of the excess fat.