The presence of Christ continues in the Eucharist as long as the eucharistic species subsist; that is, for as long as they maintain the outward characteristics of bread and wine. Obviously, if the Precious Blood is not spoiled or spilled, it ought to be consumed. (The Precious Blood is never to be deliberately poured, but always ought to be consumed directly from the vessel in which it was consecrated.)
If the Precious Blood is spilled, the presence of Christ does not continue once the point is reached when the species are so diluted with water that wine with those physical attributes would no longer be valid matter for consecration. If it does not maintain the appearances of wine, it does not maintain the presence of Christ. Like a purificator, any water used to cleanse the purificators or sacred vessels or anywhere else the eucharistic species have come to rest deserves to be disposed of in a manner suitable for sacramentals: that is, in the sacrarium or by burial, burning, etc.
BTW, this is something altar servers should know: that is, if they witness a spill of the Precious Blood, they should immediately and quickly (continuing in the calm and reverent manner proper for service at the altar) get water and a plentitude of purificators, leaving enough clean linens for any Masses that are immediately following. The containers used ought to be those suitable for holy water, purificators, and so on, if this is at all possible.