Hi @rinalds
It’s possible that you have a long field name. Please take a look at this page: http://www.advancedcustomfields.com/resources/field-value-wont-save/.
It’s also possible that your server has settings that prevent the saving process. This page should give you more idea about it: http://www.advancedcustomfields.com/resources/limit-number-fields/.
Could you also do a test on a WordPress’ stock theme like Twenty fifteen?
Thanks!