We know that novices and accepted are generally kept from fraternizing with men so they don't end up getting pregnant as that would interfere with their studies. AS may eventually become so used to being single that they become less interested in pursuing a relationship.

There's also maturity to consider. AS are around 30 by the time they're raised to the shawl. Men who have the same maturity as an AS at that point are likely either married or not interested in settling down, and an AS may not wish to get involved with someone less mature. Also, keep in mind that a new AS is still pretty inexperienced in relationships since she's spent a number of years in seclusion during which most young people actively court each other. On the flip side, many men who are familiar with AS are at best wary of them, so that probably lowers the pool of potential partners as well.

Ajah rules may play a part. The Blue for example, forbid marriage (but ostensibly not sex ), and other Ajahs might either frown upon or forbid marriages or sexual relationships. I can see Red having such bans in place. Green is the only exception that we're aware of. However, since there have been debates among AS as to whether their lack of children is contributing to a decline in channeling ability, we can probably assume that at least some Ajahs in addition to the Green don't forbid sex. Ajah politics might have some role here as well, a husband and children might create divided loyalties, which the Ajahs liekly don't want.

It doesn't seem to be a big problem with the Green, but they generally seem to stick with Warders and Warders are sworn to obey their AS, and she can fall back on coercing him through the bond. I wouldn't be surprised that the Green might have some sort of secret weave for contraceptive purposes though, since it's a bit strange that they have no observed children. Perhaps it's an Ajah rule given their role the whole "Battle Ajah", they might wish to prevent children from being orphaned should the AS die in battle.

Even then, there does seem to be a largely spinster culture in the WT as a whole that tends to discourage relationships, largely due to the extended lifespan. There's repeated mentions of AS watching not just their husbands and children, but great-grandchildren and later descendants grwoing old and dying. Not necessarily specific examples of this happening, but given as a reason for why AS avoid relationships. Possibly at sometime in the past, marriages and families may have caused various difficulties to the point where the AS tried to discourage them.

I don't think the Oath Rod itself prevents procreation. We know that AS do (if rarely) have sex. Also, in Manetherin, the Queen was always an AS, and presumably the realm had dynastic succession. So that does indicate the likelyhood of children (though I'm unsure as to whether or not the Oath Rod was in place at point). Other AS in the past were queens or other rulers, so likely they would want dynastic succession as well. Dynastic succession doesn't necessarily need to involve having children (e.g.: the WT trying to get Moiraine on the throne of Cairhien in NS; even though she's a Blue and can't marry, she would probably either produce an heir outside marriage or be succeeded by another member of the Damodred family when her rule finally ended had she gone along with the WT's attepts to put her on the throne), but it does make it easier to secure succession.