Hang on a sec... Looks like X recommended a LiPo battery (lithium polymer) and the ECX AMP does not have an electronic speed control (ESC) that provides low-voltage cut-off protection. LiPo batteries are great: lighter, higher-energy density (more powerful, lasts longer), and they rarely get hot with use so after runnining you can immediately put them back on a charger. However, they require more attention and care than the NiMh (Nickel Metal Hydride) battery pack that came with the AMP. The trade off is that NiMh batteries are heavier and have a lower-energy density and have a higher internal resistance (they don't last as long, and heat up quickly requiring them to cool down before you can recharge them).
If you run a LiPo battery below a certain voltage (approximately 2.8V per cell or 5.6V for the pack) you will ruin the battery for ever and possibly cause it to combust (burst into flame) if you attempt to re-charge it. NiMh batteries can be run completely flat without issue.
To prevent this your car needs either a "LiPo compatible" ESC (this means that the ESC features a voltage monitor that will stop the car once the battery reaches its low-voltage threshold), or a Low Voltage Alarm which is a little gizmo that plugs into the balance lead of the LiPo battery and will sound a LOUD alarm once the pack reaches a pre-determined low-voltage. This lets you know it's time to stop driving the car.
The ECX AMP cars DO NOT feature ESCs that are "LiPo compatible" so you will need to buy a LVC alarm such as the one below.
This
Venom brand LVC is fairly typical: they read out the current voltage of the pack and each cell and will also beep loudly when low-voltage is reached.
You can also just stick with NiMh batteries but purchase one with a greater capacity than was included with the AMP (A 1800mAh capacity pack, I believe.) Look for a NiMh pack with a capacity of at least 3000mAh for longer run times.
You'll probably also want to get a better charger if you don't have one. I recommend Hitec brand as I've had good luck with both the chargers themselves and Hitec service. There are many other brands such as Venom, Dynamite, Team Orion, Turnigy, ad nauseum that all offer basically the same thing.