Question about outreach

I’ve been sending around 15 cold DMs per day, and I’m no longer struggling with the initial messages—I’m actually getting a good number of responses. However, I’m having trouble keeping the conversation going.

A lot of the people I’m reaching out to already work with a copywriter, which makes it harder to build interest.
Even when the conversation starts naturally, some prospects just stop replying. I send follow ups later, but it doesn’t seem to be enough.
Whenever I try to steer the conversation towards a sales-related question (e.g., "Are you facing any challenges?"), they go silent.

I’ve accepted that some people simply won’t reply or continue the conversation, and that’s fine. But I also feel like there’s something in my approach that could be improved.

I’d love to hear from those who have mastered the transition from friendly chat to a real business opportunity. How do you keep the conversation alive and move it toward a sale without scaring people off?

Thanks in advance!

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