What I think is, there needs to be a power source to store and maintain data of any kind, be it cloud storage, hard drives, or biomolecules. Currently, the ultimate power source is the Sun. Solar energy does not depend upon humans and neither on the disturbances happening on Earth. Also, the Sun is currently the longest-lasting source of energy. Therefore, whatever solution we come up with, it should be dependent on solar energy. Since the Sun is more permanent than anything, it could be used as a basis for the physical storage equipment as well. Nothing can be stored directly on or near the Sun. Therefore, using Sun's gravity is the next best thing. With the current technology, we could build satellites that use solar energy and revolve around the Sun. A safer trajectory could be identified for its revolution and it could be launched along with all the necessary information we currently have. Communication might be an issue at times when the satellite is far away from the Earth but since the satellite is self-sustaining, it would go on its trajectory and come near to the Earth once every few years.
The trajectory and speed of the satellite could be adjusted so that the Sun, Earth, and satellite lie on a single line at every time point in its revolution. This ensures that it will be closer to Earth at all times but not dependent on it.