Why do people regain weight on low carb diets?

There's no clear definition of a low carb diet.  The variants from Atkins to different versions of Paleo have a range of views on macronutrient ratios.  They all have lower carb levels than SAD, the Standard American Diet.

Some, like a few Paleo flavours and Protein Power advocated by Michael & Mary Dan Eades, include high levels of animal protein.

Others like vet, Petro Dobromyskyj, of Hyperlipid advocate high fat levels.

Some variants of Paleo including the PHT, the Perfect Health Diet, allow 'safe starches' such as taro, sweet potatoes and rice.

Most seem to agree that all or most grains are unhealthy and should be avoided.

All seem to agree that fat and saturated fat are healthy and desirable.  Most recommend avoiding industrial seed oils and margarine.  Coconut and olive oil as well as butter are commonly favoured.

On many diets, not just low carb, people often report weight regain after a year or so.  Some attribute this to slackness and deviation from guidelines.  We may fool ourselves into thinking we don't eat a lot, when appetite has crept up.

Endocrinologist, Dr Robert Lustig commented that low carb diets are useful for weight loss, but are difficult to follow in the long term.

Jimmy Moore dismissed this until he begain to regain weight on his version of low carb, which at one stage involved consumption of red meat 3 or more times a day.

Dealing with weight regain is tackled in different ways depending on the initial health history of the author and/or their commercial interests in differentiating their particular diet.

Former doctors and current kitchen appliance vendors, the Eades, suggest that weight gain occurred when people had too much berry fruit and vegetables.  They also advise women to reduce cheese consumption as this can sabotage weight loss efforts.

Heart surgeon, Dr Steven Gundry also suggests people eat less cheese, but strongly recommends a gradual reduction of animal protein to modest levels.  He avoids cow's milk products and advocates goat's milk products.

Formerly obese, Jimmy Moore, now advocates a constant state of ketosis with high fat levels and regular ketone testing.

Jenny Ruhl, a diabetic who focuses on blood sugar control, advises people to measure and restrict calorie intake.  She also comments on problems faced by menopausal women, where depleted oestrogen levels are associated with retention of belly fat.  High fat intake may lead to weight gain.  She quotes pioneer low carb treater of diabetes, Dr Richard Bernstein, who found that some health conditions, such as polycystic ovary syndrome could play havoc with blood sugar levels.  He also noted that some forms of diabetes do not respond to dietary changes.

Researcher, Paul Jaminet, suggests that underlying health conditions may sabotage weight loss and health regain.  He advocates investigation and treatment of parasites and gut problems.

A number of bloggers in the field, such as psychologist Seth Roberts, consider that weight gain/loss/maintenance depend on our set point.  This metabolic 'fat thermostat' may be affected by the types of food we consume.  They suggest that the set point drives hunger and weight gain unless we alter it.  Seth Roberts suggests that flavourless foods can recalibrate the set point, as they are not associated with calories.

For me, it's not a question of how to lose weight initially.  

People have lost weight on a variety of diets over time.  High salad, moderate starch and low fat works well for some people.

The bigger issue is what to do if and when some of that weight is regained.

In my experience the initial tactics for weight loss may not work so well a few years down the line.  As Jenny Ruhl says, this may be associated with changes as we age, particularly hormonally.  Others suggest that our enzymes don't function as well in later life.