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Are you using the phone's browser to view/visit and play videos or audio files on your phone? Or are you using an app downloaded from the Store? Please confirm which app are you using to download them as well.
Are you getting any error when you're trying to play or download them on your phone? If yes, please provide.
What internet connection are you using when doing this? Wi-Fi or mobile data connection? Verify that it's active by browsing any websites via phone's browser.
When did you start to experience this in your phone? Are you accessing the YouTube application? Or are you accessing this via the web browser? Aside from it, are you experiencing this with other apps? Try rebooting your device by switching it off / on and observe if it will make any difference. Let us know the outcome of this.