Jobber users how are you handling new requests that don't respond after the first contact?

Two built-in options can keep that list clean. On plans that include Automations, Settings > Automations has "Automatically archive requests", which archives a request after a set number of days if it was never converted to a quote or job. Archived is a final status, and the client can't see it.

Until then, log a note each time you reach out. A request's History panel shows every edit and note, with who made it and when, so it's easy to tell who has already been contacted.