Without more detail, I would have a good look at the stock chest and pipe work, probably nothing wrong with the pump.
1. Does the stock enter the chest via a pipe system discharging above the chest level, if the stock is free falling into the chest it maybe entraining air putting the pump off-prime momentarily.

2. Does the chest include an agitator? If yes, check to see if it is beating air into the stock at reduced stock level, again putting the pump off-prime momentarily.

I assume you are maintain tight consistency control on the stock, ie., stock consistency is not fluctuating up and down although the normal low stock consistency to a head box probably wouldn't cause flow variations - more likely inconsistent / variable finished product weight.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

Are your valves responding properly. Sticking or valves that are moving when PLC not telling them to will produce swings in stock flow.

Air is stock is also a cause since pumps will cavitate.

Please explain how air in stock causes cavitation.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)