You state that "warning labels are framed based on what is known at the time it [the drug] is approved." That statement is imprecise, at best. After a drug is released by the FDA for use by the public, if the patent holder is aware of potential side effects, the patent holder is required by law to update the drug labeling. Thus, the drug label in fact changes with time.
However, generic manufacturers are not bound by any such requirement. Thus, if a generic manufacturer learns of a hazardous side effect, they are not required to update the warning label. The situation becomes potentially dangerous to the public when the original patent holder leaves the market. At that point, no one is responsible for updating warning labels and there is no mechanism for updating warning labels.
It is true that by changing the rule the FDA could be opening generic manufacturers to potential lawsuits. However, by not changing the rule, the public may be placed in danger. Which approach is ultimately in the best interest of the public? Your statement indicates that you think they public is just going to have to suffer through as best as they can without knowing about all the dangers a drug might present. That seems unfair.
It seems reasonable to place primary burden on maintaining warning labels on the original patent holder during the life of a patent. After all, the patent holder gains from having the patent, so they should also bear the responsibility. Once the patent holder leaves the market, the generic manufacturers need to take the responsibility to the safety of the drug, even if it increases the costs of generic drugs.