Each increase of 1 percent in real disposable personal income per capi

You have yourself effectively answered your own query.
The passage implies that A causes B.
C is not mentioned in the passage.
The passage implies that something other than C (i.e. A) causes B: this is option E. (However this option does not imply whether C can or cannot cause B - it just states that something other than C causes B.)

In option E, the cause C is stated as "ideological positions of the candidates". It could have been any factor other than cause A (change in real disposable income).

Argument says :
increase in disposable personal income impacts results of presidential elections. So it can be safely conclude Ideological position of the candidate is not the only thing that impacts the result of presidential election. Choice E precisely does the same. Hence, E is the answer.

Can anyone explain why the answer is not A?
I get the rational of E, but why can't we infer that an incumbent is likely (i.e. has high probability) to win when running for office?
We are told that only one incumbent lost since 1952, can't we infer that the probability of an incumbent to win is thus "likely"?

mba20202022
First, a broad principle: inference questions are asking for something that is definitely true based on what we've read. So in general, be careful about any answer that tries to predict the future based on past trends. Any such prediction relies on the assumption "If things go like before . . ."

As for the particulars of this case, notice that we were never told that only this one incumbent lost. We're told that 1952 was the only election year that saw a drop in disposable income. We don't know how much of a rise (if any) occurred in other elections, so we don't know how big an edge the incumbents developed, and we certainly don't know anything about who won.

Each increase of 1 percent in real disposable personal income per capita will increase the share of the electorate for an incumbent by about 2.2 percentage points, other things being equal. Since 1952 there has been a decline in real disposable income during only one presidential election year. The incumbent lost that election.
Which of the following conclusions can be properly drawn from the statements above?
(A) When an incumbent runs for office, he or she is likely to win. (Incorrect: no relevance)
premise is about income increase and decrease hence conclusion should be linked with winning + Income

(B) Political parties should take care to put forth a candidate who seems prosperous. (Incorrect: out of scope)
What the party should do does not matter. It should be about income plus winning possibility

(C) Presidential candidates should put their greatest efforts into improving their public image. (Incorrect: extra premise)
The premise cannot become a conclusion

(D) Because a presidential campaign requires the expenditure of large amounts of money, it frequently impoverishes a candidate and his or her supporters. (Incorrect: assumption)
Based on premise, it is assumed however inference means to conclude based on premise

(E) The outcome of a presidential election is substantially affected by factors other than the ideological positions of the candidates. (correct option)
To conclude, it needs at least two premises. This option includes both hence the best option