Research indicates that for members of congress to be reelected to office for a second term what is required is that the success of an earlier election campaign be repeated and that their voter base remain informed about their legislative achievements.
Required is subjunctive verb so "be repeated" and "remain' is correctA. that the success of an earlier election campaign be repeated and that their voter base remain informed about their legislative achievements
CorrectB. to repeat the success of an earlier election campaign and that their voter base remain informed about their legislative achievements
We can not use infinitive here.
2nd after and "that" so parallelism issue.
C. repeating the success of an earlier election campaign and keeping their voter base informed about its legislative achievements
forced parallelism and no subjunctive. Wrong
D. that the success of an earlier election campaign be repeated and that their voter base remains informed about their legislative achievements
1st clause is correct but 2nd clause "Remains" is error. Wrong
E. a successful repetition of an earlier election campaign and the informed remainder of the voter base regarding legislative achievements
Meaning change.