I don't know about any new evidence, but the case that Washington was infertile is pretty solid. Martha had children with her first husband, four times over, so we know she was capable. She married Washington at the start of 1759. They were both twenty-seven at the time, so not too old for her to have had more children. The first order to England after the marriage, included Spanish fly, an aphrodisiac. So they were probably trying.

If it's not her, then it's got to be him. Since his relations didn't have any trouble with reproduction, it's probably acquired infertility rather than something he inherited. Biographers usually point to the case of smallpox and maybe tuberculosis (he got something that laid him up after the pox) that Washington picked up in whilst in Barbados with his brother. George wasn't so sure himself. He told people that if Martha died he would probably not have any kids, but that's because he would marry someone his age. It's possible that her last pregnancy had some complications that rendered Martha infertile, but there doesn't seem to be any evidence for it. We know George was sick.

Incidentally, the fact that Washington would not father a dynasty (though his adoptive grandson tried to act the part and the Custis family were very protective of his legacy) probably helped in the creation of a strong executive. Everybody knew the first president would be Washington, however little he liked the thought. They could maybe trust him with the powers of the office, many of which he informally established, but who knew what would happen if he had a son to inherit them? No natural son meant no problem with that. Washington treated Martha's kids and grandkids as his own, but they weren't perceived as heirs to George in the way that biological children might have been. They were Custises, not Washingtons.

Sources

Chernow's Washington: A Life