There is not a one size fits all answer to this one. There are many factors to consider when relaxing fine hair. How you schedule your relaxer touch-ups depend on these things :
1. Hair growth
do you have at least 1 inch of growth? For some, that could be 6 weeks, for others 10 weeks or more. Having at least 1 inch of growth would provide room to apply relaxer to new growth only, therefore reducing the chances of overprocessing. Relaxing on less than an inch of hair growth can lead to overprocessing and thinning.
Depending on your hair texture, you may be able to stretch for longer periods of time.
With fine hair textures, most relax at 8 weeks. I choose to stretch for a least 12 weeks to ensure enough growth to limit overlapping.
Fine hair breaks down more easily by chemicals, so you must make sure to move quickly when applying to avoid overprocessing and breakage.
If you have fine hair and decide to stretch, it must be done with patience. Stretching relaxers on fine hair is a challenge. You will have to treat your hair with extra special care, when washing, conditioning and styling.
My personal feelings on when to relax fine hair is to stretch as long as possible, which is for me 12 weeks. After 12 weeks it gets very difficult to work with my hair without tangling and breakage, some may be able to stretch for longer periods of time, but relaxing less than 6 weeks would most likely cause overlapping and overprocessing.