My Vamo and Zmaxes all shut down at about 3.4 volts, not really sure what type of Ego you are using, whether it is regulated or unregulated.
Regulated should put out the same voltage until the end, then it will let you know it needs recharged.
If your Ego is regulated at 3.7 volts, it should put out 3.7 volts no matter what the battery charge is, meaning your actually battery charge could down to 3.4 to 3.2 volts and the Ego will still try to boost it to 3.7.
Unregulated will put out whatever the battery voltage is. Mechanicals do this, the
joyetech Ego C upgrade can be run in either unregulated or regulated mode.
"The eGo-C upgrade battery: is the newest improvement of Joytetech. Based on the present eGo-C battery, this upgrade battery has the new function mode --- battery voltage output mode (variable voltage output mode). In this mode, the voltage will change as the battery power changes instead of constant 3.3v output. With high voltage, this will give you a better vapor feeling.
You can also change the mode easily for your choices following the steps shown below:"
Source, Joyetech.com
Joyetech eGo-C Upgrade Battery