New around these parts, hoping someone can help me with my Mac?

I have a MacBook Air 2013 11-inch and it has started doing very random reboots. Totally random - at worst it was doing it every few minutes and currently it isn't doing it at all.

I reinstalled Mavericks and this didn't do anything. Unsure why I try reinstalling again but that seems to have solved it? But I can't see how.

There is an EFI update I found online for this model which addresses random reboots. However this update had already been applied to the machine.

Any ideas? I'm concerned at how frequently it was doing it. Yet now it seems to have gone away completely. I'm uneasy though as I can't work out why it would be perfectly fine now?

Thanks in advance and hopefully someone can shed some light.