Does anyone know of a package that can send reminders to authors when content goes stale? So like you can schedule an alert for 3 months, and if that page has not been updated in that timeframe it sends a reminder. Other CMS's have similar packages but I haven't found anything in the Umbraco marketplace but thought I'd ask to see if anyone knows of anything before giving up.

I think Umbraco Workflow does that https://marketplace.umbraco.com/package/umbraco.workflow

We have something for this, but it's a prive package unfortunately. It's called content expiration and is for hospitals who need to update certain content at least every year for compliance reasons. But I think workflow can give alerts, like @skttl mentioned. I think that's your best bet