Allow more time to pass than the time between your first follow-up.
Offer something new. Drip-feed them information so that you can send emails with new information every time.
Scrutinize your previous follow-up to see if you missed anything important, like a clear call-to-action.
Refrain from sending emails that terminate a relationship. Accept defeat by desisting.
Remain cordial, and try not to use language that shows frustration or passive-aggression.