I've been looking into this problem with slow/no weight loss for people with thyroid problems. There are a few sites that offer some info.
It seems that carbohydrate intake affects thyroid hormone function and release. Another issue is that thyroid hormone is released in a circadian rhythm with much higher release at night. Another problem is that a rapid change in diet can cause problems.
It seems that by not cutting carbs too much too quickly and perhaps using meal timing it may be possible to optimize fasting in cases of underactive thyroid.
One site suggests that 16:8 fasting may work. In this situation you aim to have a 16 hour complete fast and are allowed to eat during an 8 hour eating window (basically finish eating at say 6pm, skip breakfast and then have lunch after 12 next day and dinner before 6pm). They recommend ensuring that the eating window is during the afternoon rather than the evening as the daylight may be beneficial.
Another site suggests not letting carbs go below 20g per day.
I wonder if it would be worth trying the 16:8 approach, perhaps more often than twice a week but with a bigger calorie allowance that includes some complex carbs.
If you were to do 3 times a week with an allowance of 1000 cals in the eating window, you would be getting the same calorie reduction as with 5:2. If that works well you could try dropping to 750 cals to get a bigger calorie reduction which might be necessary with thyroid issues.
Of course there are no scientific studies at all to support this, just the experiences of people on other fasting regimes!
Thoughts?
Info came from here:
http://perfecthealthdiet.com/2010/12/in ... hyroidism/
and here:
http://drcate.com/going-low-carb-too-fa ... imbalance/