The concept of a field in physics is different from the concept of electromagnetic radiation. In the case of electromagnetic radiation, energy is indeed radiated away from the source as photons, resulting in a loss of energy and, according to the principle of mass-energy equivalence (E=mc²), a corresponding loss of mass.
Fields, on the other hand, are mathematical constructs used to describe the distribution of physical quantities (such as gravitational force or electric and magnetic fields) in space. Fields are not "created" or "destroyed" by their sources in the same way that radiation is emitted or absorbed.
When a source creates a field, it doesn't typically lose mass or energy in the process. The source may need to expend energy to establish or maintain the field, but this doesn't result in a diminishment of the source itself. The field represents the influence or potential for interactions with other objects or particles in the surrounding space.
For example, consider the gravitational field created by a massive object like a planet. The planet itself doesn't lose mass or energy by virtue of creating the gravitational field. Similarly, a charged particle creating an electric field doesn't lose mass or energy in the process. The field exists independently of the source and can interact with other objects or particles without causing any diminishment of the source.
So, while electromagnetic radiation involves a loss of mass/energy by the source, the creation of fields doesn't generally result in a diminishment of the source itself.