Whenever I navigate away from a dashboard, the filters I've set are lost. Is there a way to save them to that they remain set when I come back to the dashboard later?
Yes, you can retain the filters you have set on individual dashboards by turning on the Save Dashboard Filters setting.
In addition, you can also set persistent filters, which are filters you can set that apply to all dashboards, and which are saved to your browser so they are retained between sessions. To learn more, see this article.