Hi and welcome!
My experience of low calorie dieting, and very low calorie dieting mirrors yours. Always successful weight loss, followed by heart breaking regain. Almost as though my body wanted to bob back up to the max weight it had ever been.
Many people around here have had great success with the Newcastle Diet and the 800 calorie Blood Sugar diet, but if you have an established history of yo-yo weight loss then regain, then I would think very carefully before getting on that merry go round again. My advice would be to try and lose weight sllllooooooowwwwwwwllllllyyyyy. It may take longer, but it is so much kinder, and makes the chance of regaining much less likely. And yes, I eat Low Carb, High Fat, and love it. I have lost about 25 pounds over 2 years on it, which probably seems very slow to some. But I have not regained a single pound in that time. No yo-yo, no cravings, no aggro. And I have never gone hungry either. I am now trying Intermittent Fasting too, in the hope of nudging my weight down a bit more, but my aim is always sloooow but sure.
Others find their weight loss goes much faster, but then I have other health issues that affect/slow things down.
Do you have any other health issues like polycystic ovary syndrome, or thyroid, anything else that might be affecting things? For some of us, hormonal 'stuff' is the biggest barrier to weight loss we have.
Have a watch of this video talk by Sarah Halberg. She is an obesity doctor, and she tells it how it is.