The greatest nail in the coffin of Theistic Evolution is that Evolution requires death before sin, whereas the Bible presents death as the punishment for sin. Death cannot have existed before Adam sinned, and therefore, Evolution simply couldn't have happened. But Theistic Evolutionists think they have an answer: That only applies to human death.
Of course, for the more extreme believers in Evolution, that still doesn't solve the problem. Adam's parents would still have been human, so where do we go from there? Were they sinless? Did they not have human souls? Why would they die naturally, but Adam magically gained immortality, which he swiftly lost? Already there are too many problems. But ultimately, the Bible all but explicitly states that animals were likewise immortal prior to the fall, and that the fall affected them, too.
We actually see this, at least in part, in God's words to Satan after the fall. Cursed are you above all livestock, He said. So the livestock, and all the beasts of the field, are also cursed? And by this same Fall event, at that?
I am willing to grant that the Bible does not explicitly say "no animals died before the fall". But it also doesn't explicitly say that Jesus pooped. We do not need explicit statements when the statements we do have renders all alternatives positively asinine.
To have animal death prior to the fall is contrary to the idea that death entered the world through sin. It is contrary to the fact that the whole creation was affected by the fall. It is contrary to the very nature of God. Theistic Evolution requires so much eisegesis that it wouldn't be worth bothering with even if it were not for the fact it is utter heresy, and a sin against God. The Church of Jesus Christ of Latter Day Saints has far more credibility when they claim we existed as spirit children of God before we were born as humans than Theistic Evolutionists do when they make any claim that the Genesis account of origins is not historical narrative.