Yup, with such a low ohm cartomizer, you don't really have a need to be any higher than 3.5 to 3.7 volts honestly. Your using 1.5 ohm cartomizers right? Those are designed to pull more power from a battery and they work best at lower voltages. If your using them at higher voltages, your giving your battery a double whammy of battery sucking power. But, heres whats perplexing me... Your only using it at 4v which is pretty low already... I'd say, if this continues to suck your battery even at a low voltage beyond your expectations, try returning the battery and let them know that you'd like them to send you a replacement. It almost sounds like this MAY be a case of a faulty battery.
ALSO, did you charge your battery to its full capacity as soon as you unpackaged it BEFORE using it? I ask because we're using lithium ion rechargeable batteries and they have a charge memory just like our childhood's effect our personality in our adulthood more than any other time in our lives, haha, your batteries first charges and first uses will pave the way for the charge it will hold in the future. You should always charge your battery as soon as you get it, all the way to FULL capacity, and then always use it until it is dead, for the first 3 to 5 times, so that the internal memory will remember its highest charge point, and its correct discharge point. If you pop it on the charger before its done completely discharging the 1st few times, the battery MAY 1.) only charge to the point that the manufacturer charged it (usually 50%) and 2.) It may believe it needs to be charged when it reaches the point you put it back on the charger the first 3 to 5 times you charged it. Newer batteries shouldn't really have this memory problem because the newer ones are being programmed to know better, haha, but I have heard that this CAN sometimes be a problem.
If you continue to experience problems, send it back for an exchange or store credit refund within 10-15 days of purchasing it, and if your vendor is a GOOD/KIND vendor, he should honor this exchange.