There is no limit for saving fields in a field group.
Each time you save, all fields are updated and this requires PHP memory, vars, database calls and time.
It is possible that your server is not allowing the sufficient resources needed for the save to complete. The max_vars is a good place to start, but it is important to make sure that this value is being used by your server. Please google how to test server info such as max_vars.
Here are some similar threads:
Hope that helps.
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