Can a mild case of herpes with no open sores still infect your sexual partners?

Yes! Sometimes those who know they are infected spread the virus between outbreaks, when no signs or symptoms are present. This is called "Asymptomatic Transmission." Many genital herpes infections are spread from persons who are asymptomatic "Shedders" of the virus. At the University of Washington, researchers found that even 10 years after being diagnosed with HSV-2, adults continue to shed virus nearly 14% of days.

If sores aren't present, then there is about a 10% chance of spreading herpes from male to female and a 4% chance of spreading herpes from female to male (less mucous membrane on the penis, more on the vagina) due to viral shedding. And you never know when this viral shedding is occurring; it happens silently.