I don't want to get into contemporary politics and I'm by no means an expert on this topic but the short answer is because Ike was not a movement conservative nor was he embraced by the movement conservatives of his day. In the 1950s under Eisenhower it was not entirely clear to then-contemporary conservatives that the Republican party was a conservative party. Russell Kirk's incredibly influential The Conservative Mind essentially makes the case, if by no other means than in the diversity of the party affiliations of his selections, that America never had a naturally conservative party.

In trying to establish such a conservative movement and party, National Review (founded in 1955), under William F. Buckley, perhaps the most influential American conservative of the 20th century, was deeply split over whether or not to endorse the Eisenhower/Nixon ticket. Buckley captured the conservative ambivalence towards Eisenhower with his pithy comment:

The danger posed by the Republican Party today lies bare-breasted in its universal emblem, I like Ike. It should read, I prefer Ike.

It's also worth examining some of your assumptions about what a conservative ought to like about Ike:

He was also an advocate of a balanced budget

Sure, but the budget he was balancing was effectively a New Deal budget, which Buckley characterized in his description of Eisenhower policy from that same essay as:

easy and whole hearted acceptance of all that came before, of the great statist legacy of the New Deal

Which was, in effect, merely a "measured socialism" appealing only in comparison to the more radical program of Adlai Stevenson.

Moreover, the means by which he balanced that budget was with a marginal tax rate of over 90%.

Nor do I think the "Military-Industrial Complex" was an appealing argument to Cold War-era conservatives. First of all, it wasn't a winning argument. Kennedy (and Democrats at large) caught Nixon (and Republicans at large) on the back foot over the issue of the supposed missile gap. The winning political issue for most of the Cold War was not the military industrial complex, it was Kennedy's Missile Gap, or Reagan's "Peace Through Strength." Moreover, that was far more in line with the position of American conservatism in the second half of the 20th century.

So I think it's worth bearing in mind the divisions that existed throughout the 20th century between the Republican Party and the conservative movement. The latter of which sought to transform the Republican party from one which nominated Eisenhowers and Nixons to one that nominated Goldwaters and Reagans.

Eisenhower, in contemporary conservative analysis is viewed quite well, but he's also viewed much better by liberals. As rough and tumble as the Adlai Stevenson campaign against Eisenhower was, and as much as Stevenson was beloved of the 1950s left, today even the American progressive left will reference the positive qualities of the Eisenhower administration.

For the conservatives of the 1950s however, Eisenhower was more or less emblematic of the kind of candidate that they did not want for the Republican party, i.e. a somewhat more palatable democrat, rather than a true movement conservative.

Sourcewise:

The above quotes from William F. Buckley's essay Reflections of Election Eve as quoted here.

NB Pace Richard J. Hofstadter I've left out mentioning the John Birch Society's conspiracies that Eisenhower was a communist as, given Buckley's "reading them out" of the conservative movement, I see at as a separate question. That being said, to discuss them as part of the conservative movement would merely be to reinforce my point that Eisenhower was not beloved by his contemporaries in the conservative movement.