Our school puts them in Chill Out at lunchtime. This is also an option - children can choose chill out of they feel they need it. There is a limit on how many times they choose this.
I would have an immediate meeting with the SENCO at your school to see how they can support him in these crucial periods.
Also, they should have an appointment set up to see an educational psychologist, and following that a behavioural paediatrician. He needs a thorough assessment and possibly a statement.
What does his IEP say about how the school should support him in break times?
Actually there is no set limit before permanent exclusion can be sought. One criteria is if staff or children are at risk of serious harm. BUT. The panel would need to be shown that the school had done everything it could to help the child first.
In one example, a boy was excluded for causing injury to staff. However he had also been put through counselling, therapy, music therapy, etc. Also the school had tried a number of internal exclusions and temporary as well.
Permanent exclusions starts with a governor's panel. If they agree with the school, then you can appeal and this is heard by a tribunal. In your son's situation I would be surprised if they permanently excluded at this point, and if they did I would expect you to win at appeal.