I used to be an ALPA rep. It is a lengthy process to get someone fired for non-dues payment. At ASA we had (have) several members who have owed thousands of dollars for years and they are still here. The fact is that they have to send everything via certified mail, and if you send them $1 a month they can't touch you.
But do call your rep and discuss it with them. National is useless, all they want to hear from you is "I'm sending my check". Don't waste your time talking to National.