How to stop photo stream shutting down?

You can't stop it. Read this article --> Information about the My Photo Stream shutdown - Apple Support

There is no way to stop it. Embrace the future and remember all the drawbacks that the feature had:

• Photos from iOS devices were a lower resolution
• No Live Photos
• No Videos
• Only stored for 30 days
• Editing Photo Stream photo did not update original
• No Apple Watch support

Since the feature was launched, more people are using Live Photos and the fact it did not work for Videos is a deal breaker for most people.

It is not possible, it's an Apple decision.