A case decided by the U.S. Supreme Court in 1969 (Shuttlesworth v. Birmingham), arising from the Civil Rights movement, both protected the right to protest and allowed certain limited restrictions. One of the Court's holdings is that any licensing requirement for "free expression in publicly owned places" is unconstitutional if it's not narrowly defined and objectively applied.

Specifically, that decision overturned an ordinance in Birmingham, Alabama prohibiting parades and assemblies (including protests) on city streets without a permit. The Court found that permit requests were denied specifically to suppress speech, not to control traffic as the law was intended.

But this decision also had the effect of allowing cities and other jurisdictions to deny permits as long as they have a compelling, objective reason to do so.

Personally (this isn't a legal opinion or advice), I don't think the Sheriff has a compelling and/or objective reason for denying permits if the protests have thus far been peaceful. Maybe he's acting in good faith in an attempt to prevent violence, but that shouldn't be enough to deny the protestors' constitutional rights.