Answer
In the 56th verse of the 18th chapter and in several subsequent verses, the Lord is speaking in the 'first person singular' — in the 'I' voice. Therefore, it was natural for Him to say 'mat-prasadat' in verse 56, meaning 'by My grace.'
But by the time He reaches verse 61, the Lord begins speaking about 'Ishvara' (God in the universal sense). There He says that Ishvara dwells in the hearts of all living beings. Here, the mode of expression changes. Shri Krishna is certainly a form of Ishvara, but Ishvara is not confined to Shri Krishna alone; Ishvara existed even before Shri Krishna's incarnation.
Therefore, when speaking about 'Ishvara,' the pronoun used for Him will be 'He' (third person). That is precisely why, in verse 62, referring to that same Ishvara, the Lord says 'by His grace' — that is, by taking refuge in that Ishvara who dwells in the heart, a person attains supreme peace. This is the reason that here, instead of 'mat-prasadat' (by My grace), it is 'tat-prasadat' (by His grace).