OK...so what do you have working right now?
Do you have elite agents doing voice normally a-ok?
Do you have presence agent people working fine for chat and email a-ok right now?
Is it just when trying to do all 3 that you have issues?
Normally, if your agent is auto-answer, they go to an aux-work state if on-hook because there's no way to get them a call automatically if on-hook.
If you're not auto-answer, then manually answering the call is required - either by the agent pushing the button on the phone, or theoretically in your Presence Agent client, or your Presence Agent client would turn it to auto-answer by automatically pressing the button on the phone when the phone is ringing.
Are you sure the agent is moving to a logged out state vs an aux-work state after the point they're available and a call fails to hit them? Usually you just get put into aux-work if you fail to answer a call presented to you - like you went on-hook in auto-answer mode, or if you failed to answer a call presented to you in manual answer.