I'm sorry to hear you've been experiencing problems with network datasets in SDE. This workflow is supported. If you can describe in detail the problems you're experiencing or call Esri's Technical Support to report them, we can get them fixed.
One of the biggest issues is rebuilding it. Sometime when you rebuild it most existing edges disappear and make the network unusable. Another big issue is using it in a versioned environment. A built network does not post as built so any changes don't get recognized in the parent version, which makes it not routable. Any suggestions or solutions?
This sounds sort of hard to diagnose by GeoNet, but it definitely sounds like a problem we ought to look into. I suggest you call Support. They can work with you to either resolve the issue, or they can but it together into a bug report so we can fix it.
Out of curiosity, are you accessing your SDE network dataset through ArcMap or ArcGIS Pro?
I've always been of the opinion that feature datasets misbehave in the enterprise environment, so I've avoided them.
What advantage do you see keeping it in the enterprise environment?