I don't know if the urge goes away.
It hasn't for me. We have two children, a boy and a girl. Everyone from our neighbor to my mother has assumed we're done. I wasn't sure right away. I even thought maybe we were done. But for the last two months or so, I've been feeling that urge again.
Right now is not the right time to have another. My husband's job isn't as secure as we'd like, and he is working much longer hours than I am used to. We just moved across the country and don't even have a pediatrician yet, much less an OB, and I'm not close to family anymore. Plus, a third would make flying back to see the folks harder, it would make vacations harder, and it would make international travel (something Hubby and I plan to do the moment the kids are old enough, since we have been WAITING to get back to our travels ever since our first child was conceived) much more difficult. Our house has three bedrooms, so while we could fit another, the kids would have to share rooms. I'm not even sure how I feel about going through the newborn phase again, or changing the wonderful dynamic in our family. Hubby and I haven't agreed on whether or not to have a third, but we've both agreed that now is not the right time.
But the urge to add a third is pretty intense for me. I don't know if that baby craving vanishes once you hit the number you want in your family - I always wanted more than 2 kids, so maybe my body is just waiting to hit that magic number. Or will I just keep craving another and another? I am enjoying reading the other responses. Maybe I'll find an answer in them, too.