Transimpedance Amplifier Behavior With Supply Voltage
When you had split +/- supplies the current source injected its signal relative to 0V i.e. halfway between the power rails and of course the op-amp will prefer this. 

In your 2nd setup you are injecting you current source relative to the most negative rail (again 0V) but how can the op-amp produce a negative voltage under these circumstances? The data sheet indicates that the op-amp cannot be relied upon to produce a sensible output voltage within 100 mV of the most negative rail.

Try biasing the non-inverting terminal to mid rail by using a resistor potential divider.