Tosafos seems to say that we have to make sure that a person dying who is giving a gett to his wife does not loose his cognitive abilities in between the writing and the giving since that would invalidate the gett. The Maharsha asks that he doesn't know where Tosafos gets this from. Although he must retain his mental state for the writing and during the shlichus of giving it to her, why should he have to be in a good mental state in between the two? The Beis Yosef agrees with the question of the Maharsha and therefore stretches Tosafos to be saying that he must be in a good mental state during the time of the giving of the gett. One may have thought that the fact that he improves after the giving the gett would indicate that he was in a good mental state when it was in fact given, to which Tosafos says that we cannot rely on that assumption. Based on this the Beis Yosef holds l'halacha that he does not have to retain a good mental state between the writing and giving. Beis Shmuel (121:5) suggest l'chatchila being machmir for Tosafos, but me'ikar hadin agrees with the beis yosef.
The Rashash justifies the simple reading of Tosafos that he must remain mentally stable from the writing thru the giving. The rashash compares this to dichuy by mitzvos where we have a discussion whether if something is pushed off whether it can become fit once again. However, the rashash doesn't directly address the question of the Beis Yosef, that the Mishna implies that kurdaykos i.e. bad mental state, doesn't ruin his original command to write the gett, certainly it should not ruin a gett which has been written. The Taz (121:4) takes the same approach as the rashash, reading Tosafos as it implies, not like the Beis Yosef, and therefore requires his mental stability in between the writing and giving. He responds to the question of the Beis Yosef by saying that if someone had only commanded to give a gett the shlichus begins only when the sofer begins to write, so if he would loose his mental abilities before the writing begins and then become cured, it would not invalidate the shlichus. But in our case where the gett is already completed and ready to be given, if he would loose his mental abilities so that it could not be given at that moment, the gett is invalid at that time and cannot be fixed by restoring his mental ability.