As I understand it, which admittedly is limited, the RE gravitational theories also have some problems with not quite matching with observations. Are they going to be thrown out or are they going to be modified? The UA is a young theory and most probably not completely understood.
Yes, they are thrown out in those situations. That is why Newtonian Gravity is used in engineering, where things travel nice an slow, but not in modern physics.
GR has its problems as well, but the biggest one I know of is that it doesn't mesh with quantum physics. If you think about the scale of the problem, it is like expecting an understanding of dust mites on peoples eyelashes to predict the stock market. The two theories work on very different length and time scales, but they work well in their own regions.
I worked on a project that is trying to better understand neutrino mass. Not so many years ago people were convinced that neutrinos were mass-less and the standard model was shaped to fit that idea. New experimental evidence suggests that neutrinos do have mass, so a new 'version' of the standard model with new (modified) mathematical equations is now being explored.
If theoretical physicists have their way both GR and Quantum will be thrown out and replaced with one theory that explains all observable length scales.