The debates about prisoners losing US citizenship rights—a condition sometimes called “civil death”— includes numerous factors. One must consider who a prisoner is and what constitutes citizenship-related rights.
The category of “prisoner” includes a wide variety of individuals. The US penal systems includes both state and federal components. The offenses which are punishable by imprisonment range from inability to make bail to felonies such as homicide, and sentences range from a few hours to multiple life sentences. There is considerable variation among states regarding the relationship between a crime and a given sentence. It is also possible for people to be detained and held in prison before they are convicted of the crime of which they are accused. Another factor to consider is how citizenship was acquired, by birth or naturalization. Conviction of a crime can result in citizenship being stripped from those who were naturalized. Furthermore, not everyone who is in prison is a US citizen. Therefore, there is no single recommendation that would cover all these disparate situations.
The other part of the question relates to what constitutes US citizenship. Rather than being one single right, citizenship includes a large number of different rights and privileges. People who are incarcerated as part of their sentence after having been convicted of a crime do lose some of these rights and privileges. One example is the First Amendment freedom of peaceable assembly, which is generally not allowed in prison. Another significant right that is denied to many prisoners is the vote. There is widespread debate about disenfranchisement while serving a sentence and upon release, whether for completion of the sentence or on parole.