We built an engine for scratch for the terrible F2P game Dino Park (released on Android but not in the US). We used it on the even more terrible National Geographic's Dino Land on iOS. Both of which seem like they are no longer available, which is probably a good thing because they were unfinished and had terrible pricing. (Not my fault! We worked with a publisher) Chris did the art and Joe did the animation, which were both awesome.
The tech we made was solid, and the Neverending Nightmares engine is an evolution of that. As we continue to develop games, less and less of the original remains. For Neverending Nightmares, we wrote a sound engine, a World Builder, added a ton of AnimationTool features, switched to SDL, so there isn't THAT much that still remains.
We are definitely continuing to build on our current tech because we were happy with it. Post NN, we have added more Animation Tool features for Joe, improved the World Builder, etc. We are making significant changes on the gameplay side too.
Writing a new engine from scratch is a lot of work, and there aren't often better ways to solve problems, so I think even most people going from PS3->PS4 aren't starting over.
Assuming we are making games that are mostly 2D, I think we'd stick with our engine. If we wanted to go full 3D, then we might use Unreal or something just because there are a ton of solved problems that wouldn't be worth doing our own way. We might consider Ogre or some open source 3D engine, but it'd probably be a lot of headaches especially for porting.