iPod touch Refurbished 4G iPod touch Battery issues

Hi,

Recently I purchased an Apple Certified Refurbished 4th generation iPod touch on ebay. Upon charging the device and quickly fiddling around with it, I noticed the battery seems to be draining extremely fast. For example, I fully charged it last Tuesday (3/26/13) and today I cannot start it up. It displays a red battery indicator. It has been on standby the whole time. I only turned it on 2 times to check the standby time. Halfway through this process, I checked the usage and standby time and it showed that it had 4 hours of usage and 4 days of standby time left.

To give you some background info:

- BT is off

- WiFi is on

- iTunes wireless sync is on

- Push notifications are on (I do not receive that many on my other devices)

- iCloud backup is on

- Mail is set to retrieve manually

These are the same settings as my two-year-old iPad 2, which does not have this issue.

Is this battery life behavior normal for the 4G iPod touch with the above settings enabled or does it appear I am having a problem?

Thank you very much!

Yes, my 2G iPod touch, even though it does not have all the features, such as iCloud and WiFi sync, that could drain the battery, actually has better battery life after 4 1/2 years.