I have an Intel HD graphics 4000 and I can say that this GPU never worked well for rendering with Eevee.
I have already fixed a lot of issues with Intel HD graphics 4000 but some of the solutions are not feasible.
The render crashes if the Screen Space Reflections and Ambient Occlusion are enabled.
The problem is that, with this option enabled, Eevee generates shaders that require 11 uniform samplers.
In a single rendering context these shaders work fine.
But when rendering with F12, blender creates another rendering context to run on another thread and apparently the limit of uniforms samplers allowed in the shader (that must be about 20) is reduced by half for this GPU configuration. (10 < 11 = crash)
I can not think of a good solution, but we can workaround this problem by using View Render (F11).
Another thing we can do is wait for a solution from Intel and update the drivers.