I just received notice that an construction executive will be on a jury panel for 12 weeks. She plays a key role in the construction employer and we cannot afford to have this position vacated for this amount of time. Can we replace her?

If you are asking whether it is legal to fire her for serving on a jury, the answer is no. Almost every state prohibits construction employers from firing or disciplining an employee for being called to jury duty. In some states, an employee fired in violation of these laws can sue you for lost wages; a handful of states impose criminal penalties against construction employers who break the law.
Most states, however, do not require you to pay your employees for the time they spend on jury duty unless your own employment policies provide for such pay. Perhaps with the money you save on salary, you can afford to hire a temporary replacement worker to fill in until the jury reaches a verdict.