I am running Mavericks 10.9.2 with Keynote version 6.1. Since obtaining this Mac in January the OS and Keynote has never crashed and works reliably; as do most users systems.
try this repair, if that doesnt work your system is unstable and you should clean install Mavericks.
repair tasks for Keynote 6.1 ensure you complete all the tasks and in the order shown:
1 delete all the iWork applications if you have them, not just Keynote by using Appcleaner from Mac Update to do this, its freeware
2 restart the Mac; Apple menu > restart
3 immediately after the start chime, press the shift key until you see the Apple symbol.
let it fully boot up, it will take longer as the OS is repairing the drive
4 when fully booted, go to Applications > Utilities > Disc Utility; click on the boot drive then First Aid tab and click repair disc permissions
5 when complete, restart the Mac normally
6 install Keynote from the Mac App Store
Please report back to let us know if this helped.
There were several other issues and other programs crashing. Since this is a 1 month old laptop, I took it to the "Geniuses" and they reinstaled Mavericks.
This seems to have fixed the other problems I was having with the laptop. If it doesn't end up fixing Keynote, then I'll post again here for others.