Follow-ups work because most people simply miss the first message, not because they rejected it. A good follow-up should feel helpful and polite, not persistent or pushy. Reference your earlier note briefly, then add something new such as an insight, example, or quick benefit.
Space follow-ups a few days apart and keep the tone relaxed. Short messages outperform long ones. If you are sending multiple touches, vary the angle each time. If there is still no reply after two or three attempts, step back and move them to a nurture track rather than continuing to push.
Simple bump
Style: minimal, no pitch