iPhone only forwarding a few, random, notifications to watch.
My first thought would be that it's a connection issue. Have you noticed any other symptoms that could also be explained by that possibility? 

Also, you could go through the process of unpairing and then restoring your Apple Watch to see if that resolves the issue. See: How to unpair and restore the Apple Watch.

Another option is to call Apple Support. They can actually run diagnostics on your Apple Watch remotely (you will need to have your iPhone with you as well in order for them to do this). It doesn't take long to do and will help identify if there are any hardware issues.