Typically I do not use rapid fix on fiber prints. Rapid fix is better for film however. My process for fiber prints is 1. Developer (2-3 minutes), 2. Stop bath (30 seconds), 3. Fixer (32 oz Sodium Thiosulfate and 4 oz Sodium Sulfite to one gallon of water for 4 minutes), 4. Second fixing bath same as first 4 minutes, 5. Selenium toner (1-4 minutes), 6. Hypo clearing agent for 2 minutes, 7. One hour wash in Zone VI print washer.
The second fixing bath that I use today will be the first fixing bath tomorrow.
I have found that rinsing between the second fixing bath and selenium toner does create unwanted staining of prints. However as I stated I do not use rapid fix in my print processing. Perhaps your process is adequate in light of that difference.