Below is a biological answer to your question. I am not commenting on the health and diet of the doe because I believe it is the more understood than the biological side. I hope this helps bring better understanding of what nature throws at us.
What you are asking about is called lactational anestrus, which is a lack of cyclicity brought about by nursing and presence of the young (or fawn). Lactational anestrus, like many other things, has not been heavily studied in white-tailed deer. What we do know about lactational anestrus are principles found in all mammals. The female mammal’s body is designed to ovulate in preparation of reproduction. White-tailed deer have what is called seasonal anestrus, which is a period of anestrus (lack of cycling) induced by either long or short photoperiods (days). This seasonal anestrus is designed to give the doe enough time to achieve pregnancy, birth, lactation, weaning, and recovery by inhibiting the cyclicity of the doe before her next ovulation.
The simple answer to the question is the tempting “It Depends”. Lactational anestrus is dependent on two factors; 1) the frequency of the doe being suckled, and 2) the presence of the doe’s fawn. The first sixty days a fawn is suckling is the only time in which a doe will be in true lactational anestrus. This is to give the fawn on the ground the greatest chance of survival. After the initial 60 days frequency becomes the main focus. The fawn suckling on the doe stimulates the release of an inhibin that suppresses the release of hormones by the brain to start cycling (estrus). This not only includes the amount of times a fawn suckles, but the total number of times in which any of her fawn suckle. The point in which the fawn is pulled or weaned, the lack of stimulation allows for the release of estrus initiating hormones, starting cycling (estrus). The second factor that causes lactational anestrus is the presence of a fawn. The visual, auditory, and olfactory (smell) senses given off by the fawn are known to stimulate the doe “mentally” increasing the chance of inhibiting hormones causing lactational anestrus.
Both of these factors, frequency and presence, CAN cause lactational anestrus. As stated above, the only true consistent factor is the first 60 days of suckling. We need to be aware that we are dealing with nature and a perfect creation that will never be truly understood (but is greatly marveled at). Since all of the deer in our pens are being provided with the highest level of nutrients, we have to look at the biological factors to make the decision of AI-ing the doe or not.
As I see it we have a couple options…
1) Start the AI process and “see what happens”
2) Pull the fawn ASAP and bottle feed the fawn
3) (next year) Pull the cover buck/ AI earlier to prevent late fawning.
4) Not AI-ing the doe.
Hope some of this makes sense. If you have any question or comments let me know.