If children are either born innocent or not held accountable for their sin, then why do children die?
For the same reason that born-again Christians die. Not because they are spiritually dead, but because they are in a world subjected to futility (Romand 8). Jesus said, though you die, you will live.
Physical death is not an indicator of spiritual condition for anyone - adult or infant.
They die because of what the first Adam did by bringing death into the world. (Rom.5:12-14
They inherit his nature.
They do not suffer spiritual death because of what the Second Adam did (Rom.5:15-21)
The issue is rejection of the free offer of grace.
If a child is not old enough to make a rational decision to believe on Christ, he remains under the blood until he is (Jn.16:9)
This means also that mentally retarded people are all saved since they cannot make a rational decision to accept or reject Christ.