You go to your Package Center and your packages don't load at all. The error is Connection failed. Please check your network and time settings.
The problem is the URLs required by the Package Center can't be resolved.
There are a few issues that can cause this. They include the following:
Synology's Package Center Is Down
Before you do a bunch of troubleshooting, make sure the Synology service is available. Do you get a 404 or other errors? Is it down for everyone or just you?
Your Time Setting Is Inaccurate
Go to Control Panel > Regional Options > Time, tick Synchronize with NTP server. Select an NTP server and click Update Now to make sure the time shown on your Synology NAS is correct.
IPv6 Is Disabled
Go to Control Panel > Network > Network Interface > edit > IPv6, change the setting from “Auto” to “Disable.”
If you don't want to disable IPv6 in DSM, go to your router and make sure IPv6 is enabled. This was the issue for me!
Besides the occasional downtime, the problem is most likely with your network configuration. You may need to play with DHCP or MTUs. If you run an IPS or a Firewall, be sure to check if you are blocking Synology domains, especially connections to Taiwan!
If the problem wasn't one of the 3 issues above, let me know in the comments below what the problem was and how you fixed it!