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Below, I have included some basic troubleshooting articles for this issue.
However, this sounds like a possible issue with port blocking, a firewall issue or older password protocol on the router side. This articles below cover recommended ports for using Home Sharing, the Apple TV and recommended wireless settings. If you are unable to edit the setting on the Wi-Fi access point, you may need to contact your ISP to make the adjustments and check for router firmware updates.
Also, here is an additional resource for troubleshooting issues with the Remote app.
Hope that helps,