What is the rationale for not making the Sign of the Cross after receiving Communion?
Let us start with the liturgical Rite of Pope Pius V. In the Extraordinary Rite of the Mass the priest sign the recipients of Holy Communion immediately before receiving the Sacred Host which by the way was always received while kneeling. The Faithful never signed themselves in the Old Rite.
As the priest places a Host directly from the chalice into the mouth of each communicant, he prays for life everlasting.
Holding the Sacred Host in his right hand, the priest makes the sign of the cross with it and says:
Corpus Domini nostri Jesu Christi custodiat animam tuam in vitam aeternam. Amen.
The following YouTube video explains how a priest performs these sacred actions in very clear detail (1:42:00 and following): The Latin Mass Explained and Demonstrated for Priests.
We can notice two things here. The priest made the sign of the cross just before the recipient received the Sacred Host and he did not bless himself afterwards.
The priest as the minister of Holy Communion blessed us with the Sacred Host as we made our communion and now that we have received Our Lord with that same Sacred host there remains no real reason to bless ourselves since we have God residing within us. We have in a sense become a living tabernacle and dwelling place for the infinite majesty of God's presence for the duration of time that the Host remains within us. This is Catholic teaching that is universally accepted mystery of faith.
There is no need to bless ourselves at communion because we truly have Jesus within us?
The rubrics found in the General Instruction Of The Roman Missal (Vatican source) for the Mass of Paul VI do not call for the faithful to cross themselves after receiving Communion. If a person wants to do it, as a personal act of piety, there is nothing that stops him, however. However this is not a tradition liturgical expression of faith. I myself have never heard of any priest insisting or teaching that we should make the sign of the cross at communion time.
Many priests may teach this as a pious act of Catholic piety, but it is in no way a traditional act of Catholic piety.
The Church simply asks that we receive Communion reverently, either by slightly bowing before receiving (if we receive standing up) or by kneeling (which is always an option). Communicants should respond with “Amen” when the minister says, “The Body of Christ” or “The Blood of Christ.”