Can my husband's ex-wife file abandonment charges even though he pays child support?

The state where the ex-wife and children live is Arkansas. This is also where they filed for divorce. We currently reside in Tennessee. He pays child support weekly but she will not allow him to see his children or even speak to them on the phone. He tries to reach contact with them daily. It has almost been a full year since he has seen them (besides a birthday party she was kind enough to invite him to). We are saving to take her to court, but I am worried as I do not fully understand child custody laws. She has remarried as well, and probably wants my husband completely erased from their lives. Is there something that she can legally do that would cause him to lose his children without intervention or being forewarned?