The Archive has a certain amount of precognitive ability given the amount of knowledge it has access to. I suspect Ivy has long had a plan to have a child and worked out her own highest probable moment of death, and planned to have her child before this.
That said, I suspect should the Archive be killed without an offspring, that's it. I imagine that's a tempting target for the enemies of the Archive.
Which is why the Archive has a bodyguard, and many allies invested in it's protection.
Ivy is a rare case I suspect - she inherited the Archive as a child. Most times the Archive would probably only get passed on to an adult child of the previous vessel of the Archive. Which allows the next one to grow up and have another child, likely before receiving their inheritance. So Ivy is a bit of an unusual (perhaps unique) case. But she will have planned for it. But with who is the question.
I don't think that the bearer dying without an heir would lead to the construct's destruction. If it did, there's no way in hell the Archive would EVER be doing field work like in Death Masks, much less going into actual battle, like in Battle Ground. Though it's entirely possible Ivy already has a daughter or two. While it's uncomfortable to think about, it's entirely possible the Archive would compel its host to have a daughter as soon as biologically possible and safe.
I doubt Ivy has any children yet, given she is hardly out of childhood and as far as we know has no attachments. I don't really see Jim not raising this in the books. It would be logical for there to be a compulsion, but I also suspect there is no need beyond any natural biological compulsion. Free Will and all that.
And I disagree about the Archive doing field work. Ivy certainly didn't have a child during Death Masks (I'd bet anything on that). But Ivy did have Kincaid, and is sort-of a demigod in her own personal power (the warden's files rank her around the same level as the Ladies, and Harry thinks they under rate her by a bit). I think she took a calculated risk in that scenario and wasn't too worried. Remember, Nicodemus had to get help from Lucifer (well, it was apparently more like one of his lieutenants who provided the actual power) for the Signs that helped capture her. It isn't that easy to take out the Archive.