You are a mother who has full custody the paternal grandparents go for months at a time with no contact can they still get their rights?

If you reside in a state that recognizes grandparents rights, the grandparents are legally within their rights to petition the court for visits with the child, but even if those visits are ordered there will be a schedule set by the court that they will be required to follow. Grandparents visitation rights are much more limited than those of a parent, and your responsibility as a parent ends with making the child available for scheduled visits. If the grandparents miss visits or do not follow the requirements of the order with regards to when the child must be returned or the setting in which the visits take place you can petition the court to have the visitation suspended. If the grandparents don't bother to go to court, or you can show that visitation with them is detrimental to your child based on previous contact then you don't have to hand over your kid just because they ask or demand.