I guess birth control in the future is still unreliable or Picard's Borg implants ruined his vasectomy
The implication from GEN is Picard was sterile.
PICARD: I'd come to feel that René was as close as I would get to having a child of my own.
TROI: Your family history is very important to you, isn't it?
PICARD: Right. Oh, ...from being a small child, I can remember being told about the family line. The Picard who fought at Trafalgar. The Picard who won the Nobel Prize for chemistry. The Picard's who settled the first Martian colony. When Robert married and had a son, I...
TROI: ...You felt it was no longer your responsibility to carry on the family line.
PICARD: Right. Yes. That's it exactly. You know, Counselor, Recently I've become very much aware that there are fewer days ahead than there are behind. ...But I took comfort from the fact that ...the family would go on. But now there'll be no more Picards.
René was as close as Picard felt he would come to having a son. There will be no more Picards. Why is that, unless Picard was somehow incapable of fathering a child.