Their mothers hide them. In addition to the sheer lack of any reference whatsoever to Aes Sedai having children, to the point where it shocks the Whites when Verin turns back on them their suggestion about women bearing children by gentled men, Elayne too ran into a wall of ignorance concerning maternity effects on channeling, and vice versa. Even if a particular sister might not have had children herself, that kind of knowledge circulates among the group. You'd think that over three centuries, SOME maternal lore or secondhand information would have ended up in Vandene's mental archives.

I keep coming back to Faile's little recitation in aCoS when she and Perrin are returning from Colavaere's deposing, and she is listing historical examples of Aes Sedai subservience to the Tower's interests. All of them include familial betrayals or violations, which to an aristocrat, is the most profound sort of counter-indicated behavior imaginable. If Faile knows about women who were forced to marry (consummate said unions) or betray their royal brothers, because of the Tower's interests in seeing a certain balance of power in or among the nations, it is a given that the sisters know about them, and probably others that outsiders were never allowed to learn about.

With that knowledge, I would bet that a lot of sisters shy away from marrying anyone other than a Warder, who is protected by Tower custom (and being devoted to his Aes Sedai, a Tower loyalist/asset by transitive property), and also refraining from bearing children. Note that the Blues have a specific custom against marriage, though Nynaeve and Elayne refer to no such custom or restriction among the Yellows and Greens (and they would have noted it, given their romantic status at the time of their ascensions; also the sisters, even those who might have held back some Ajah lore until they were "really" raised, would certainly not have kept silent about restricted or disapproved-of behavior, especially something as hard to undo as marriage), and the Blues are the most ideologically driven and politically active and motivated. No one is going to ask a soldier or Healer to sacrifice her children to interests arising from their vocations, but politicians on the other hand...

The children of Aes Sedai, having access to superior material and educational resources, even if they can't channel, would have considerable head starts in life. Even those who don't have titles from their Aes Sedai mothers or noble-born fathers (and nobles, even in the post-medieval society of WoT, would still be the most likely candidates to have attained the necessary skills of a Warder, especially at a young age), would, with their mothers' stations and connections, have a relatively easier time marrying into a noble house, or being granted a title. Any way you look at it, unless one of the most powerful women in the world is willing to consign her children to a life of anonymous drudgery, they are very likely to rise to positions of importance or influence if they have any ability at all. Importance and influence means politics, which means a sister's children might find themselves in the path of a Tower strategem and the mother or grandmother in the position of those women Faile mentioned.

If Aes Sedai are actually having children, in spite of the dangers of that course of action, and the time being taken, and attention diverted, from their all-important plots and schemes, they are almost certainly keeping it on the down-low. And by "they" I don't mean the Tower, I mean the women giving birth. The best way to prevent the Tower from asking you to sacrifice a child is not to let the Tower know you have one to sacrifice. This would explain the absolute dearth of knowledge about child-bearing available to Elayne, when the sisters have other knowledge that they might never intend to use, like masking a Warder bond. Simple human curiosity leads people to ask hypothetical questions, so that sort of knowledge still circulates. But things pertaining to childbirth...any mildly curious sister who might wonder aloud where others could hear her what the effects of channeling are on pregnancy, and vice versa, would only hear crickets in reply. Either sisters would not have first hand knowledge, or they would not admit to having that knowledge, lest someone wonder where she learned it, and then wonder where she was those ten months right after bonding that sexy young warder.

Another reason for the habit of secrecy would have arisen in the hinted-at bad old days when Aes Sedai settled disputes in more exuberant & energetic fashions. A non-channeling child is a softer target than her Aes Sedai mom, to a pissed-off rival. In addition, with certain Ajahs being more likely than others to get into that particular condition (i.e. Greens and Reds, respectively), it would give one side a vulnerability that their enemies did not share.

For these reasons, I'll bet that the Tower would have a "don't ask, don't tell" custom, even more than their standard reticence & privacy boundaries, concerning motherhood and pregnancy. For the same reasons, it is likely that sisters generally forgo motherhood, but if they don't, said reasons are an even greater incentive to keep that status as secret as anything.