My battery needs service as it is not working for long. Apple claims it is not a defective battery and that it is my fault since I had the computer for 2 1/2 years and have only run the battery down to empty 100 times. It is my fault because I did no

Question

Con't
Apple claims that because I did not drain my battery frequently and kept it plugged in for extended periods of time, that it is my fault the battery is failing.  I disagree because I was not ever told to consistently drain my battery before recharging or not to keep it on and plugs in for extended periods of time.  I do keep my desktop computer on most of the time and that is why I have kept my Macbook air on for extended time periods.  I feel that Applecare should cover this battey issue and not charge me for replacing the battey.  I feel I should have been told to not keep my computer consistently running on with poweror the battery will fail.  Has anyone had this problem?  Apple should replace my battery under Apple care as my battery does not keep a charge anymore.
I'll wait to hear.

Answer 1

You said---Apple claims that because I did not drain my battery frequently
You said---  I was not ever told to consistently drain my battery before recharging
You should never do that on purpose, whoever told you that had it wrong or you misunderstood something
Sure you dont have that backwards? thats exactly what you DONT want to do.
Did you often drain the battery very low? that would explain a lot.
Someone might have been misinformed about "battery calibration" regarding much older Macs with removable batteries (see bottom)
You said-----I do keep my desktop computer on most of the time and that is why I have kept my Macbook air on for extended time periods.
thats a problem there, youre not supposed to do that.
Keeping batteries connected to a charger ensures that periodic "top-ups" do very minor but continuous damage to individual cells, hence Apples recommendation above:   “Apple does not recommend leaving your portable plugged in all the time”, …this is because “Li-ion degrades fastest at high state-of-charge”.
                    This is also the same reason new Apple notebooks are packaged with 50% charges and not 100%.
http://www.apple.com/batteries/notebooks.html
"Apple does not recommend leaving your portable plugged in all the time."
*If you don’t plan on using it for a few hours, turn it OFF (plugged in or otherwise) ..*You don’t want your Macbook both always plugged in AND in sleep mode       (When portable devices are charging and in the on or sleep position, the current that is drawn through the device is called the parasitic load and will alter the dynamics of charge cycle. Battery manufacturers advise against parasitic loading because it induces mini-cycles.)
Keep it plugged in when near a socket so you keep the charging cycles down on your LiPo (lithium polymer) cells / battery, but not plugged in all the time. When not being used for several hours, turn it off.
And best "tip" is if its near a socket,...plug it in as long as you can (especially at home) since cycle count on the battery are the "miles that wear out the tires (battery)", however again, not plugged in all or most of the time.
General rule to remember of Lithium batteries is:
Never drain them LOW  & dont always/often store them HIGH
While cycle count is commonly seen to be the “miles” on your Lithium Ion pack cell in your Macbook, which they are, this distinction is not a fine line at all, and it is a big misconception to “count charge cycles”
*A person who has, for example, 300 charge cycles on their battery and is recharging at say 50-60% remaining of a 100% charge has better battery usage and care than another person who has 300 charge cycles at say 15% remaining on a 100% charge. 
DoD (depth of discharge) is far more important on the wear and tear on your Macbook battery than any mere charge cycle count.  *There is no set “mile” or wear from a charge cycle in general OR in specific.    As such, contrary to popular conception, counting cycles is not conclusive whatsoever, rather the amount of deep DoD on an averaged scale of its use and charging conditions.
                          (as a very rough analogy would be 20,000 hard miles put on a car vs. 80,000 good miles being something similar)
*Contrary to some myths out there, there is protection circuitry in your Macbook and therefore you cannot overcharge it when plugged in and already fully charged
LiPo (lithium polymer, same as in your Macbook) batteries do not need conditioning. However...
A lot of battery experts call the use of Lithium cells the "80% Rule" ...meaning use 80% of the charge or so, then recharge them for longer overall life.
Never let your Macbook go into shutdown and safe mode from loss of power, you can corrupt files that way, and the batteries do not like it.
The only quantified abuse seen to Lithium cells are instances when often the cells are repeatedly drained very low…. key word being "often"
Contrary to what some might say, Lithium batteries have an "ideal" break in period. First ten cycles or so, don't discharge down past 40% of the battery's capacity. Same way you don’t take a new car out and speed and rev the engine hard first 100 or so miles.
Proper treatment is still important. Just because LiPo batteries don’t need conditioning in general, does NOT mean they dont have an ideal use / recharge environment. Anything can be abused even if it doesn’t need conditioning.
From Apple on batteries:
http://support.apple.com/kb/HT1446
http://www.apple.com/batteries/
Storing your MacBook
If you are going to store your MacBook away for an extended period of time, keep it in a cool location (room temperature roughly 22° C or about 72° F). Make certain you have at least a 50% charge on the internal battery of your Macbook if you plan on storing it away for a few months; recharge your battery to 50% or so every six months roughly if being stored away. If you live in a humid environment, keep your Macbook stored in its zippered case to prevent infiltration of humidity on the internals of your Macbook which could lead to corrosion.
Considerations:
Your battery is subject to chemical aging even if not in use. A Lithium battery is aging as soon as its made, regardless.
In a perfect (although impractical) situation, your lithium battery is best idealized swinging back and forth between 20 and 85% SOC (state of charge) roughly.
Further still how you discharge the battery is far more important than how it is either charged or stored short term, and more important long term that cycle counts.
Ultimately counting charge cycles is of little importance.  Abuse in discharging (foremost), charging, and storing the battery and how it affects battery chemistry is important and not the ‘odometer’ reading, or cycle counts on the battery. 
Everything boils down to battery chemistry long term, and not an arbitrary number, or cycle count.
Keep your macbook plugged in when near a socket since in the near end of long-term life, this is beneficial to the battery.
Peace
Battery calibration, battery memory, battery overcharging, battery training, …all these concepts are mostly holdovers from much older battery technology, and on older Apple portable Macbooks ranging from early nicads, NiMh and otherwise; and these practices do not apply to your lithium battery and its smart controllers.
Calibrating the battery on older Apple portable Macbooks with removable batteries.
http://support.apple.com/kb/PH14087
There is no calibration of current Apple portable Macbooks with built-in batteries.
http://support.apple.com/ht1490
There is no battery calibration with current Apple portable Macbooks with built-in batteries. Lithium batteries have essentially a 0-‘memory’, and all such calibration involve the estimations fed to the system controller on the SOC (state of charge) of the battery over long periods of time as the battery degrades. The software based battery controller knows the battery's characteristics, or SOC and adjusts itself. This is why there is both no need and purpose to periodically deeply drain your macbook battery, since it doesn’t affect the characteristics of the battery, and further still deep discharges are something you should not do on purpose to any lithium battery.