ACF checkbox values are not saving on the site. I’m having the same issue across 3 websites using 3 different themes. Hence it doesn’t look like a theme/memory issue.
I’m not seeing any issues saving checkbox fields. I would look for something common to all 3 sites. Another thing to look for is duplicated field names which could cause you issues, duplicate in ACF or field names shared with other custom fields used by anything else on the sites.
I’m currently facing the same problem with a checkbox field which I populated dynamically. I don’t have any other field or subfield with the same name. Actually i’m using Data-Key to call the field.