More often than not, the cause of the weight gain is because they fall back to bad eating habits. If you can lose it, you can keep it off. Changing to long-term good habits is extremely difficult though.
Here's one that mentions 20%. But that's at a year. The % changes depending on how long you follow up(drops all the way out to 5 years.). This is study uses keeping off 10% of body weight as the definition of success which is far less than the amount that it takes to move an individual from obese into the normal healthy range.
If you can find a study where a majority of the individuals experienced significant and long term(3 yrs+) weight loss I would be happy to see it.
Also here's a study that suggests the exact opposite, that rapid weight loss is correlated with long term success.
While I applaud those individuals that have kept off weight long term, the science disagrees that is an achievable goal for everyone.(only about 5% of people who successfully lose large amounts of weight will keep it off long term)
For example here is what happened to the contestants on the biggest loser.
https://www.nytimes.com/2016/05/02/health/biggest-loser-weig...
The body will fight very hard to get back up the heavier level. It play nasty tricks such as increasing hunger, decreasing metabolism, and nastiest of all physiologically sabotage the part of the brain that is responsible for conscience regulation of food intake(it turns off willpower specifically for food).