Pijiang - Non-Cap H1B Continuation Question

My attorney told me that since the university only pays me on a 9-month basis, I will be out of the status in the 3 months in summer unless I can change to other status and then change back to H1-B in fall semester. Is that true?

I was highly suspecious of this statement, since I will get a 3-year h1-b status approved. So my question is: is my employer required to pay my salary on every pay period? If it were the case, what alternatives do I have?

Thanks!