Bikes usually wont just die while your riding it!They will start to give you subtle warnings like sputtering or a loss of power like its running on three cylinders instead of four stuff like that running out of fuel..etc. when bikes do die immediately its usually because you accidentally hit the kill switch or the connector for the ignition switch came loose.
Bikes today usually have three ways to kill it.#1 engine kill switch #2 tilt/bank angle switch or #3 kickstand switch. i know you probably didnt hit the engine kill switch and im sure you didnt go over a bump fast enough to upset the kickstand switch. so im guessing that the bank/tilt switch is faulty.The new battery probably just reset the tilt sensor and thats how you got it restarted. All your restarting has now drained the battery and it will need to be trickled charged for at least 4 hours. Battery voltage should be 12.5v or greater at rest then check it while idling 12.8v to 13v normal, then rev up to 4k rpm watch meter should rise to 13.5v to 14v then immediately go down and hold at about 13v this is normal regulator/retifier readings. And if your battery is in fair condition you could try and see if it"ll push start and if it does (and you inspected the all the kill switch circuits) then ride the bike for about 15 minutes above 4000k to recharge the battery.

I would check your connections and grounds. I would check the voltage of the battery with the bike off and then compare it to the voltage when the bike is running to see if the battery is charging. Your may have enough voltage to run lights but not enough amperage to crank. Is the new battery full of acid? silly question but I have seen this happen before, the guy puts the wrong amount in it.
Check your fuses too. I would verify that its charging before trying to chase down any current draws of shorts.

If still under warranty, take it back to dealer and do aclaim, else check your regulator/rectifier connections, fuel flow fom tank to carb, spark plugs & wire condition, starter motor connections.

I also have the same problem just bought my brand new k9 and a week later my bike shuts down on me while riding pretty scarey knowing i almost got ran over due to this new gixxer just shut down on me, so i then hooked it to a charger and thought okay its the battery so the next day took it out for a drive angin 15min. later the brand new gixxer shuts down on me again wtf so i called the dealership and told them wat happend and they said i may of fryed the wire harness due too hooking it up to a running car but wtf does that have to do with it it shut down on me before all this but the bike still runs like new but shuts down when it gets hot but the question is if i fryed the wire harness the bike will not stare right?????????? ive been doing researches on these bikes the gixxers and it seems like this is a common problem with the gixxers they just shuts down..........like i said its pretty scary when ur doing about 50mph and the bike shuts down on you.......

I have a 2007 GSXR600 that wont start, the lights come on but the fuel pump wont and everytime i hit the start switch the light go off then on when i release it. I checked all the possibilities of battery, the three kill switches, the fuses, starter, and even replaced the tip over sensor, I tried resetting the computer by switching the key on and off, at least thats what I was told to do by a mechanic and still nothing, I am now checking the wire harness to see if there is a short in the wires and then going to check the grounding, but would appreciate it if someone has the knowledge of what could be another step for me to take, thanks.