You're right: a "hold up" (noun) is a threat toward somebody at gunpoint, almost always for the purpose of stealing their money.
However, this is being used as a verb. What they're trying to say is:
Does this theory remain valid?
How well does this theory hold true?
A car that "holds up" lasts for a long time and doesn't require frequent repair. A house that "holds up" endures natural disasters without much damage. A body that "holds up" is aged but doesn't get sick and is relatively free of disease.
As you may have noticed, when using "hold up", you first require a previous test. A trial. An evaluation. If nothing happened, you don't ask did it "hold up". It doesn't make sense. However, let's suppose that your tire popped on your car and you had to drive 10 miles before reaching a car shop. You call a friend. You tell them the situation. A question they may ask you would be, "how did your tire hold up?"
When we say, how does the theory "hold up", what we really mean to say is, "when we examine/explore/entertain/ridicule/test the theory, how true/good/valid is it?"
Hopefully that helps. I would roughly translate this sentence:
¿Qué tan cierto resulta este teoría?
¿Cómo aguanta esta teoría?