As far as the battery discharging, I would use a multimeter and check it to make sure your charging system is functioning and that there isn't unusual current draw when your bike is turned off. I hear many people say that if you don't run at least a certain RPM your battery doesn't charge. That simply isn't the case. Unless you have some unusual current draw, your battery should charge even at idle.
I have a 2000 so its possible that the 2007 is a little different but the way it works on the 2000 is that at idle, the voltage to charge your battery bypasses the voltage regulator and comes directly from the rectifier (turns AC to DC). The voltage is ~14.2VDC. That's more than enough to charge your battery. Above a certain RPM (don't remember exactly what that is) the voltage goes through the regulator and drops to ~13.7VDC. Still plenty to charge the battery. The service manual confirms this as well.
When your bike is off, if you check current draw it shouldn't be more than 20ma. I have a PC3 and a Speedohealer on my Busa and the current draw happens to be exactly 20ma. Also, if you meter the voltage with the bike off, the battery should be between 12.8 and 13.5+ VDC, depending upon if you have a AGM style battery or a traditional lead acid type.
What could cause your battery to drain are rides that are too short. It takes quite a bit of power to get the starter to turn the engine and fire it up. It takes a while of charging to "replace" the voltage that you used to start the bike. If you start the bike, ride it for 10 min, put it away, do the same the next day, etc. Eventually, the battery voltage will be too low to start the bike.
One last check, while metering the voltage on your battery, if you hit the starter and the voltage drops below 9VDC, the battery is bad, regardless of what the voltage reads without a load.
I think MC MUSTANG's suggestion about checking the idle setting is a good one and where I would start if I had your situation.