An article at Public Health Nutrition suggests that, yes, the paleo diet is one of the last to be abandoned. I’m not paying the $35 for access to the full article, so I don’t know which diets were considered. I assume all the popular ones.
Abstract
Objective: To use Internet search data to compare duration of compliance for various diets.
Design: Using a passive surveillance digital epidemiological approach, we estimated the average duration of diet compliance by examining monthly Internet searches for recipes related to popular diets. We fit a mathematical model to these data to estimate the time spent on a diet by new January dieters (NJD) and to estimate the percentage of dieters dropping out during the American winter holiday season between Thanksgiving and the end of December.
Setting: Internet searches in the USA for recipes related to popular diets over a 15-year period from 2004 to 2019.
Participants: Individuals in the USA performing Internet searches for recipes related to popular diets.
Results: All diets exhibited significant seasonality in recipe-related Internet searches, with sharp spikes every January followed by a decline in the number of searches and a further decline in the winter holiday season. The Paleo diet had the longest average compliance times among “new January dieters” (5.32 ± 0.68 weeks) and the lowest dropout during the winter holiday season (only 14 ± 3 % dropping out in December). The South Beach diet had the shortest compliance time among NJD (3.12 ± 0.64 weeks) and the highest dropout during the holiday season (33 ± 7 % dropping out in December).
Conclusions: The current study is the first of its kind to use passive surveillance data to compare the duration of adherence with different diets and underscores the potential usefulness of digital epidemiological approaches to understanding health behaviours.
Steve Parker, M.D.
Paleo Diabetic 
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