Where does it say He is offering His blood all the time?
Hebrews 9:23 Therefore it was necessary that the copies of the things in the heavens should be purified with these, but the heavenly things themselves with better sacrifices than these. 24For Christ has not entered the holy places made with hands, which are copies of the true, but into heaven itself, now to appear in the presence of God for us
It's a reference to the Yom Kippur temple liturgy (see Leviticus 16) in which the bull is slaughtered, and the High Priest then takes its blood into the Holy of Holies and offers it to God. That is an intrinsic part of the sacrifice.
Hebrews 9 applies this image to Christ, and makes it clear that his offering in the Holy of Holies is eternal (obviously, because it's in heaven, which is outside of time).
You err greatly if you think that the death of the victim ends the sacrifice. There is no sacrifice under the Law (or even before it) that was concluded by killing the victim; in every case, the victim has to be offered to God by the priest. Christ is both High Priest and Victim, thus his offering takes place in heaven, which makes it eternal.