It's your battery and frankly, I think you got lucky with the first one (unless you were using it less, and dual using cigarettes and etc.) Batteries tend to only hold a charge for a specified period of time, and the 28 day warranty tells you something-- this is designed more as a disposable device, not something you can use for years at a stretch.
It may be possible to replace the battery, but really I'd leave that to someone who knows what they are doing. I'm doubtful the company will replace/warranty without charge, and honestly, you can do much better in a device.
I agree with Letitia's suggestion, look for a small, external battery mod where you can remove the battery and recharge it, and then replace the batteries when they start to wear out. I might suggest a pico 25 mod, they currently have a newest one that uses a single 18650 battery and the size is nice, it's a very portable unit, and while it isn't "stick style" it's really a comfortable form factor in the hand. There are also lots of other nice options, but the pico is a good fit for many who are looking for a small, portable device. I might suggest buying the mod and the tank separately, as the "kit" has a Melo III tank, which isn't really so MTL in my opinion. Good MTL tanks include the Nautilus 2, or any tank that takes the Joytech CLR 1.0 ohm coils (say, the Tron-S, the Ego One Mega V2, etc.) but using those coils, not the proprietary coils that come with it. The CLR coils get great coil life and flavor, and are very easy to rebuild and rewick as well, if you get to that point.
Good luck, I'd suggest, really, moving up to a more reliable device, that has more options for resistance of coils, airflow, variable wattage, etc.
Anna