It's been an interesting month.
Since I have updated devices to 7.0.6 and killed applications not in use on my iPad Air 128Gb, the crashes has gone. Today, I updated the iPads to 7.1 and will continue to monitor the situation but I am beginning to think how applications use Apple's iOS has a large part to play in fixing this issue.
Here is what I recommend others do based on what I did with my "control" device - iPad Air 128gb, to mitigate the crashes.
1. Update to the latest iOS. If your settings -> general -> about...version doesn't say 7.0.6 or better yet, 7.1, you haven't updated your iPhone or iPad yet. Go force the upgrade by connecting your iPad to a USB port on your PC or Mac running iTunes. I recommend 7.1 because it probably fixes more security vulnerabilities which were recently reported in the media.
2. Make sure you synchronize your iPhone or iPad first. But more importantly, make sure all your apps are updated as well. In iTunes, go to Library -> Apps and hit update all and make sure everything is up to date.
3. Kill all the running apps that you absolutely don't need in the background. To do this, fast double push the home button or use four fingers to swipe upwards on your home screen to show all the applications running. Swipe left and right using one finger to show all the running apps. Swipe upwards using one finger against any application you don't need to run. You can always restart the app so make it a practice to kill apps you don't need. Personally, I have 9 apps always running - Home screen, Mail, Facebook, LinkedIn, Safari, 1password, one note, iMessage and kindle. All others, I might inadvertently leave running but when I do remember, I go to this list and kill them when they are no longer needed.
After you have done all of this (including updating and killing apps for the first time), hard switch off the iPhone or iPad. In other words, press and hold the power button until you are asking to swipe right if you want to power off. Power it back on and use the device as you normally would. Measure how long your experience lasts for before a crash.
Mine never came back. While I can't attest this will work for everyone, it worked for me. Hope this helps someone.