It's very feasible and there's probably quite a few different ways that it could have this effect.
One obvious one is hypothyroidism, have you had your thyroid checked?
Personally, I would not go down that road again as you're likely compounding the problem each time you do it.
I looked into the health risks of very low calorie diets a few years ago and listed some of the research I found here: very low calorie diet research
But the research is very short term, last I checked the health risks if VLCD's hadn't really been followed longer then 12 weeks after that they put the people straight onto a refeeding program and follow for a few weeks so long term is a very grey area. But having said that there is a lot of research in regards to starvation and these have a huge effects on your brain over the long term. There was a study a long time ago that studied the effects of men following a 1500 calorie diet over the long term and it had profound effects on their health and mental abilities and they became very obsessed with food. I can't think of the name of it right now as my partner is playing music very loud and I can't hear myself think!
However, having said that there is some research on the psychological causes of food restriction, there is one that I linked to on the bottom of that page and I keep meaning to go into this more but time is an issue. But basically it is very common for people to develop eating disorders after dieting particularly severe dieting such as VLCDs and VLCDs can even bring on psychosis.
Unfortunately, I don't recall reading much on VLCDs and memory but I definitely think this would be connected as thyroid alone can cause these problems that you're experiencing and very low calorie diets have been shown to downgrade your thyroid and you will see some of the research on that page I linked to.
Also, when I was researching this I did write a couple of articles on what I did find which you're more then welcome to have a squizz at low fat and very low calorie diets plus also I should share a great article I found on obesity online that explains the yo-yo phenomenon really well. It is a really good read: THE PHYSIOLOGY OF WEIGHT CHANGE
Sorry I couldn't help much with your question but I hope this helps in regards to VLCDS
Cheers
Sherrie