For us, the simple frequency of communication has been important. Not all prospects need our product (a hiring tool) all the time, but this way we can be top of mind when they do.
We try to communicate every week with our "dead prospects" and we bring some back to life every time.
In terms of content, we use short emails with curated content, a new post, or product updates. It's low effort to send. Product updates work particularly well as it's a chance to highlight features and benefits without directly selling.