YAY! You got in and posted!
Ok, on to your question.
As a professional advocate, one of the biggest pieces of advice I offer is "choose your battles" and I rarely recommend that you fight a battle that you cannot win.
There is nothing in IDEA or any state regs (to my knowledge) that would prevent you from being your son's para. Your school district policy may say otherwise.
However, this is not a battle that you're likely to win. A 1:1 or para may be FAPE for your child, but "school won't have to pay" should not be your argument as that is not what IEP services are based upon. They're based on the child's needs.
When you say the "teacher has stopped trying" you need to further define that, for your IEP team, and call a meeting. What, specifically, is your child not receiving that they need?