The s of sad is changed to ṣa after an upasarga (Preposition) having an i or u , but not after prati,
The word सदिः is in the first case, but has the force of genitive. Thus निषीदति, विषीदति, न्यषीदत्, व्यषीदत् ॥ निषसाद, विषसाद ॥ The second स remains unchanged in the Perfect by 8.3.118.
Why do we say 'but not after प्रति'? Observe प्रतिसीदति ॥ Prof. Bohtlingk points out that the sutra is सदेरप्रतेः as given by Sayanacharya in his commentary on Rig Veda VI. 13. I. Panini, however, often uses the first case with the force of the Genitive, as in 8.3.80.,