How do I keep my constant current source constant?
Try this: 







simulate this circuit &ndash; Schematic created using CircuitLab

This circuit is capable of ~1% accuracy with good layout. If the battery is removed, the op-amp will current limit into the base, which should not hurt it. If you don't like that, or if you use another op-amp that doesn't current limit as well, add a small base resistor such as 100 ohms.