Whenever we want to WEAKEN an argument, we must first assess the line of reasoning, and see where it is flawed.

Conclusion:
- the new drug is clearly preferable as a treatment

Premises:
- drug now most commonly prescribed for the disease occasionally has serious side effects such as seizures
- the new drug has side effects much more frequently, but the worst of them is mild nausea

Assumptions:
- the only important criteria in assessing which drug is "preferable" is the severity of side effects
- or, the drugs are equally effective
- frequent but mild side effects are preferable to infrequent but severe ones

In order to WEAKEN the argument, we must find an answer choice that attacks one of these assumptions.

A) It is possible that the drug now most commonly prescribed has side effects that have not yet been attributed to it.
This would strengthen rather than weaken; it gives us more reason to believe that the new drug is preferable.

B) People who experience nausea are prone to discontinue use of the new drug prematurely.
If this is true, then people will stop taking the new drug, limiting its effectiveness. This gives us reason to doubt whether this drug will be preferable. Correct.

C) Other drugs for the disease have typically been prescribed only for patients allergic to the most commonly prescribed drug.
Irrelevant. The conclusion is only concerned with the comparison between these two drugs, so we don't care about other (presumably less preferable) drugs.

D) People who have received effective treatment for disease do not generally contract the disease again.
Irrelevant to this argument. It gives us no reason to conclude that one drug is preferable to the other, as both are presumed effective.

E) There is a nonprescription medication that when taken with the new drug prevents the onset of nausea.
This would strengthen rather than weaken. The new drug's worst side effect is easily prevented, giving us more reason to prefer it. We need an answer that says the opposite.

The answer is B.