No. When a witness signs a will, he or she is saying that the testator has testamentary capacity. This signature creates a presumption that the testator had the necessary mental capacity when he or she signed the will. If the witness dies, this presumption stands and the will is still good.
However, at probate, a will must be proved. To prove a will, a court must determine that the will conforms to the guidelines set by law. One guideline is that the testator must have had the mental capacity to execute a will. Witnesses are needed to testify to the testator’s mental capacity at the time the testator signed the will. Of course, if the witness has died, then he or she cannot testify. The presumption still remains, but clearly the will is not as strong as if the witness could testify.
One way to avoid this problem is to have a self-proving will. A self-proving will has signed statements called affidavits attached to the will. These affidavits allow you to avoid having to track down witnesses for the probate, even if they are still living.
For more information, see: W. Va. Code § 41-5-15 (2015); Martin v. Thayer, 37 W. Va. 38, 16 S.E. 489 (1892); 20 Michie’s Jurisprudence Wills § 37 (2009).