Why can we not receive the Eucharist by intinction? At one time it was permitted. Why has it been stopped, especially in this age of communicable diseases?

Communion by intinction (where the host is dipped in the precious blood by the priest or minster and then given to the communicant) is still permitted. Hence, it would seem that the decision to end the practice is a decision rooted in your own parish.
 
Though permitted, intinction is not a very widespread practice in most parishes in America. There are likely several reasons for this.
 
First, the practice introduces a complexity into the distribution of Communion. For example, when intinction is used, Communion cannot be received in the hand, which is an option some prefer. Thus it would seem that only some stations could have intinction. This then creates further complexities about who lines up where, and how various options are explained to the faithful at each Mass.
 
Further, the practice requires either special equipment, (i.e. a paten with a small cup for the precious blood) or someone standing nearby with a chalice of precious blood. The norms also require the use of chin paten when intinction is used. None of these complexities are impossible to overcome, and intinction can be, and still is practiced, in some places.
 
As for wanting to receive the Precious Blood in a way other than a shared cup, please note that in fact you do receive the precious blood. For in the Host alone, even in the small fragment, there is contained the whole Christ: Body, Blood Soul and Divinity.
 
The use of the common cup(s) has reference to the fact that Christ shared his precious blood from a common cup. The concern for communicable disease is understandable, but not a definitive concern for most healthy people. The option always remains to refrain from partaking under that sign, and the Precious Blood is still received in the host alone.