And he might not like to see her reconnecting with Roman when she won’t connect with him.
Burgess seemingly shut down on Ruzek after her miscarriage as her way of dealing with the tragedy, not even looking at him when he came to her in the hospital and then shutting down his efforts to help after she was discharged, saying that she needs space.
He was taking it as well as could be expected, but like when she was shutting him out after he found out about her pregnancy, he may only be able to go for so long before trying to reach her whether she likes it or not.