My daughter went through a period of being afraid I would leave. She would even cry when she was left home with her dad and I would go to the store for a few minutes. She was about 4 and I was a stay at home mom.
She would even get upset when I would leave her at Sunday School. At the time I was working in the class just down the hall. She also knew all the workers as most of them were personal friends of mine that she had grown up knowing. Finally she was able to tell me that she had a dream that I had left without her. I assured her that I would not leave without her and the teacher would let her look out the window every so often and see our van in the parking lot.This did not go away quickly but it got better over time. She became less and less tearful when I would leave and eventually went to classes gladly and willingly.
As she got older she did not want to spend the night at her friends house or go on girl scout over nights. I would let her stay until midnight and then come and get her. Her friends were very understanding and reassuring. Just be patient and keep reassuring her that you will be back. Eventually she started staying at sleepovers. I think we each have our own fears and this is one of them.
My daughter is now 15 and very well adjusted. She's very social and has many friends. She just slowly grew out of this.