A specific reason is that it was a testimonial statement and the defendant cannot cross examine the child about it (she probably has no recollection for example due to her age then). That can violate the defendant's 6th amendment rights.
Here's a case (Georgia, not controlling here but maybe instructive) where a stepfather was convicted of killing his stepdaughter, where the court found that letting a police officer testify that a child said "Daddy did it" more than once in response to a question about an earlier assault on the child violated the defendant's 6th amendment rights.
"(a) On July 20, 2002, a military police officer responded to a domestic disturbance call made by the victim's mother.3  When the officer arrived, the victim had a bruise on her face and was holding an ice pack on it.   The officer, who had been trained on interviewing children, testified that when she asked the victim what happened, the victim, who was three or four at the time, repeatedly said “Daddy did it.”   In its order denying appellant's motion for new trial, the trial court found that the child's words were non-testimonial because they were in response to the officer's question as to what happened."
"The trial court erred in admitting this evidence because the victim's statements were testimonial and violated appellant's Sixth Amendment right to confrontation.  Crawford v. Washington, 541 U.S. 36, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004);  Brown v. State, 278 Ga. 810(3), 607 S.E.2d 579 (2005).   As opposed to statements made in response to garnering police assistance during an ongoing emergency (such as statements elicited during a 911 call to determine the need for assistance), here the child's words were statements in response to a question by law enforcement after the emergency had already ended and were reflective of past events and, as such, were testimonial in nature. "
http://caselaw.findlaw.com/ga-supreme-court/1230870.html
So, there may have been a hearing with that as a result. The DA may have thought it would be a losing cause and so has not tried to introduce that. Rule 403 cited above could be another reason.
Anyway, these things turn on very complicated and not necessarily obviously logical factors, so take the above with much salt. It's just to say there could be valid reasons to keep the statement out.