Our cockatiel, Precious, who had been out free-flying many times, did the same thing. She is my husband's little angel. When he went out the door, she flew after him. Instead of landing on him, she made several flights around the house and disappeared. We were horrified.
All of our birds are flock call trained. When out of sight of us, our parrots flock-call us and return our flock-calls to them. While Precious was out of viewing range, she would call and answer our calls. Soon after, Precious stopped calling us and returning our calls. We own a large piece of property in the country. We spent four hours of intense searching, calling out to her, and crying the entire time while looking for her. About the time when we had given up, she flock-called us from a distance. We went around the ponds and the house following her calls. Then, the calls stopped again. My thoughts finally collected. I realized that she quit calling because she could see us. So, we hid from view and she flock-called us.
Sure enough, she was sitting about 30 feet up in one of the big pine trees beside our house picking of bark and playing. (Little stinker). My husband and I both broke down crying. He used a PVC pipe to shoo her off the tree limb. Precious flew down from the tree and landed on my husband's shoulder. We instantly took her in and clipped her wings so that she could still fly, but short enough to prevent her from getting enough lift to fly high.
We often forget that it is within their nature to fly free. Though they are part of our flock, it is part of their instincts to want to soar and be free. As a result, we no longer free fly our babies.
It is heartbreaking enough to lose one for four hours. I cannot even imagine the hurt and suffering that you are feeling. If I were searching for one of our birds, I would put something familiar outside, play videos that have sounds of songs, and keep looking. I am so sorry for your pain and heartbreak. I hope you find your little angel.