What is the limit for entering Thailand on a visa exempt status within one year?

There is no technical limit by air for visa exempt. But it’s up to the immigration officer to stamp you in. Whether that’s 3 times or 6 is their call. No one can say what that particular officer will do.

Some come in visa exempt very regularly (they have family here and work offshore or are pilots or the like) and they get away with many entries. Some are asked on their 2nd or 3rd entry.