If my exhusband refuses to answer his phone to make arrangements to see his children, how long can this go on before he is abandoning his children? We live in Missouri and have been legally divorced over a year.

How old are ur kids? If they can, let them speak to ur ex themselves. If u know the address where he is now, let the kids write them letters, send cards, greet them happy father's day. Maybe the reason he doesn't pick up the phone, he avoids discussing things with you. So let kids call their father. And avoid saying bad things to ur kids how's their father. It's bad.

Normally abandoning is leaving them at the mall and walking off. There is no way to force an ex to see his children, he has the right to visit but you do not have the right to force him to.
Also normally just not seeing the children is not grounds for terminating his rights, is he paying child support

He's not abandoning; he's ignoring, unless he's not paying child support.