If my paraphrase consists of several sentences, should a citation for the original source appear after each sentence?
No. The citation should appear only after the final sentence of the paraphrase. If, however, it will be unclear to your reader where your source’s idea begins, include the author of the source in your prose rather than in a parenthetical citation.
For example, the following is a paraphrase from an essay by Naomi S. Baron:
Literacy consists of both reading and writing. The writing might take the form of marking up a text or making notes about it (Baron 194).
Here your reader might think that the first sentence is your idea and that Baron’s idea begins in the second sentence. For clarity, you might revise as follows:
Naomi S. Baron argues that literacy consists of both reading and writing. The writing might take the form of marking up a text or making notes about it (194).
Baron, Naomi S. “Redefining Reading: The Impact of Digital Communication Media.” PMLA, vol. 128, no. 1, Jan. 2013, pp. 193-200.