I understand why the school would want to raise the defense; however, I can think of several reasons why that defense would not hold water.
1. Numerous times, elementary schools got sued for personal injury when kids got injured during recess. This led to most schools taking down their playground equipment. Therefore, schools must not have sovereign immunity, otherwise, they could have just raised the defense, no fuss no muss.
2. They are not "the government," per se; they are largely independently-owned and operated. The money they get from the government is really nothing but a glorified affirmative action program. They should have no more sovereign immunity than the Post Office does.
3. During my google search, I did not find any conclusive information, but I DID find that several states have passed statutes that state that public schools have sovereign immunity. If a statute is necessary to state this, then it would stand to reason that, in the absence of said statute, schools DON'T have it. Therefore, without any such statute in Arkansas, it would stand to reason that a public school is still entirely vulnerable.
What do you think?