"Suppose I were drowning, and you drew me out of the deepest water, just in time to save my life, but then left me wet and shivering and exhausted on the bank, to run the more than risk of wretched after-effects of cold and rheumatism, from which I might never entirely recover! That would not be saving 'to the uttermost' in this sense of the word. But if you did the thing completely,-carrying me home, and doing everything necessary to restore me, and avert ill effects, and that effectually; never relaxing in care and effort, nor letting me go, till you had me safe and well, however long and difficult it might be, then you would have saved me 'to the uttermost,' in the true meaning of it.
This is what Jesus is able to do for you. Your first coming to Him is only like letting Him grasp you in your terrible danger, and draw you out of the fatal depths. But 'because He continueth ever,' (Hbr 7:24) always the same loving and faithful Saviour, He will complete what He begins. For we are 'confident of this very thing, that He which hath begun a good work in you will perform it until the day of Jesus Christ.' (Phl 1:6) Having saved you from destruction, His very name is the guarantee that He will not leave you to struggle helplessly with your sins, (Mat 1:21) much less to 'continue' in them, but that He shall save you from them. You will find it a daily continual salvation, by which He will keep you by the power of God through faith, unto the consummated salvation of body and soul, 'ready to be revealed in the last time.' (1Pe 1:5)"
-- Frances Ridley Havergal
"But this man, because He continueth ever, hath an unchangeable priesthood. Wherefore He is able also to save them to the uttermost that come unto God by Him." (Hbr 7:24-25)