Not from an expert, but since no one else has responded ...
Are you in a drought condition? It could be your well is not pulling in the water it once was or that sulfur has started to contaminate your well. It's interesting that if you use a lot of water, the odor fades only to return later. It could be you have a contaminate in the well that tends to settle and when you pull a lot of water, it temporarily runs the contaminant out.
I would allow the system to sit overnight, then flow enough to clear the pipes and test the water directly from the well and test the water from the outlet of the softner. Run a lot of water until the odor fades and repeat. Your water conditioning people should be able to tell from the results if your resin needs replacing. The second test should tell you if something is building up in your well.