How is your signal strength?  If the nearest tower has been shut down
for maintenance or something like that, your phone may be using more
power to maintain contact with a more distant tower.  Of course it may
be something else entirely.  Are any of your neighbors having similar
problems?

We can't troubleshoot your phone by remote control, but I'd like to put
in a word about Lithium-Ion batteries and your problem.....

How long do you think your car's battery would last if you only charged
it once a week, instead of whenever you could (by driving the car).  
Lithium-Ion (Li-Ion) batteries have characteristics very much like lead
acid car batteries....They LOVE to be FLOATED at full charge....and HATE
to be left discharged any longer than is absolutely necessary.  The more
ofter you charge them, the longer they will run.  They do NOT, as some
wives tales would have you believe, have 500 charges or 1000 charges
before replacement.  That is simply NOT true.

What Li-ion batteries DO have is a built in custom IC in each battery
that PREVENTS you from discharging them past about 50% of full charge.  
If they are deep cycled, they are not recoverable, so the manufacturers
invented this cheap little chip that monitors the current and voltage and
shuts down the battery before you damage it by discharging to to
oblivion.

This IC has a little problem....It loses its way.  When that happens the
IC shuts down the battery way too soon, before it should, and you hold
your hands to your head and say, "Oh, nuts!  The battery's bad."  This
isn't necessarily true and here's the cure......

Charge the battery up full charge over night.
Discharge the battery as far as you can with the phone shutting itself
down...after all those warning beeps.
IMMEDIATELY recharge the battery overnight.
The little IC will reprogram itself and sync itself to the real state of
the battery and reset it's turnoff point.

You might try this on the old battery you never restarted, too.  You may
not have destroyed it with this run-it-for-a-week bragging rights
nonsense.

RECHARGE YOUR PHONE EVERY CHANCE YOU GET.....even if it's only been
running for 6 hours.  If you see a charging cord hanging off your desk,
do the little guy a favor and LET HIM DRINK!  If you do that, Li-ion
batteries will long outlast the phone itself.  It's quite simple.

I run my Z6m battery down at least once a day because of the Nokia N800
Linux tablet using it for a modem all day long.  But, even if it's not
discharged, I recharge it every time it's near a recharge cable.  The
tablet's battery is similarly recharged often....

Works great....Just don't brag to your buddies you do it and you'll be
fine....(c;