E6530 intermittently won't boot

I have a Latitude E6530 and about half the time when I power it on the laptop shows the Dell logo then hangs. Then after about 30 seconds it turns itself off. If I turn it back on it starts just fine.

Once the laptop has booted, I can repeatedly shut it down and power it on and it will be fine. But if I leave it a few hours then half the time it won't boot.

My guess is it's something to do with the disk, but I've tried with two different disks (one mechanical and one SSD) and both show the problem. I've tried setting the disk mode to AHCI and Raid, and both show the problem. It doesn't make any difference whether the laptop is on the mains or the battery, but either way it only happens after the laptop has been off for a while.

This isn't a big deal, since the laptop always boots (at the second attempt!) and works just fine, but it's annoying. Can anyone suggest what might be causing it, or any checks I can run to try and identify the cause? I've thought about contacting support (it has support till December) but since the problem is intermittent it's likely to be hard to replicate for the engineer.