MacBook – replace the old model MBA battery with a 54-watt-hour lithium-polymer battery (12 hrs) for the newest model MBA

I have the same Air as you and I am getting 5-6 hours. So not to much off of what the advertised amount is. Your battery sounds faulty to me.

The last computer I had had a faulty battery. It was replaced for free and within a couple of days. Back then they simply replaced the battery on the MB because it was removable. Chances are now they will give you a new laptop because the battery on the Air is harder to remove. You might be without a computer for a few days though. I don't know what they do in other countries, but in Spain they just took it and mailed it to Holland to get fixed and then mailed it back.

The first step is to look at the detailed battery information from the System Information/System Profiler for each battery.

  Charge Information:
     Charge Remaining (mAh):     5587
     Fully Charged:              Yes
     Charging:                   No
     Full Charge Capacity (mAh): 5611
  Health Information:
     Cycle Count:                289
     Condition:                  Normal
  Battery Installed:          Yes
  Amperage (mA):              0
  Voltage (mV):               12420

Pay attention to the Full Charge Capacity and cycles for each battery.

The second step (assuming my guess that you have a non-unibody Mac where the battery is user-replaceble - swappable without removing the bottom of the Mac) is to run a simple calibration charge cycle on the new battery (and followed by the old one perhaps to compare). Once your computer gets to know the new battery (it guesses based on average battery performance until it determines the chemistry particular to each battery that gets used over time).

The third step if you really want to measure everything on both batteries is to use the pmset -g pslog command to document each battery as it powers your Mac from full to the low power shut off point.

Here is the relevant section from the man page linked above:

 If your system suddenly sleeps on battery power with 20-50% of capacity
 remaining, leave this command running in a Terminal window. When you see
 the problem and later power and wake the computer, you'll be able to
 detect sudden discontinuities (like a jump from 30% to 0%) indicative of
 an aging battery.