When the Kiyor was not submersed at night and as a result the water became posul, was there a potential remedy, such as to reinsert the Kiyor into the 'well' and be 'metaher' the water through a 'hashokoh' process, or did it have to be emptied and refilled?
Sh, London
Tosfos (Zevachim 21a, DH Kiyor Kivan) writes that it is only effective if one immerses the Kiyor before the water became Pasul, but if the water had become Pasul, the Gemara (Pesachim 34b) states that there is no "sowing" (Zeri'ah) for Hekdesh. Tosfos there (Pesachim 34b, DH v'Nasan) writes that Hashakah is not effective for Hekdesh.
While Tosfos there in Pesachim writes that is a Torah Din that Hashakah is ineffective for Hekdesh, I should point out that Rashi there (Pesachim 34b, DH Ein Zeri'ah) disagrees and writes that the Din that Zeri'ah (which is the same as Hashakah) does not work for Hekdesh is only a Ma'alah (a higher standard) that the Rabanan imposed for Kodashim, but it is not a Torah Halachah.
Tosfos in Zevachim 78b (DH Ha d'Rabei) also writes that the Din that Zeri'ah is ineffective for Hekdesh is a Chumra b'Alma.
I suggest that one may add a majority of kosher water onto the Pasul water: While we have seen that Pesachim 34b states that they made a Ma'alah not to do Hashakah on the sanctified water that became Pasul, I want to argue that one may add on 51% of kosher water so that we will now have a kosher majority. Even though we generally have a rule, "Ein Mavatlin Isur l'Chatchilah" (see Beitzah 4b), we are not allowed to intentionally annul an Isur (for example, one is not allowed to pour kosher wine into non-kosher wine until one obtains a permitted mixture), nevertheless in the case of the Kiyor water that became Pasul this is not actually considered as Isur, since it is only a rabbinical Ma'alah, according to Rashi in Pesachim 34b, and one may add on a majority of kosher water (see Rashi to Zevachim 78b, DH Malei Mei Chatas).
Kol Tuv,
Dovid Bloom