Leaving the computer running is actually better for the long term health of the system, so long as it's adequately cooled. Turning the machine on and off sends voltage spikes through the boards that can cause wear on the the components and even fry them. That's actualyl a common problem with all electrical devices, and why so many of them seem to always die right when you turn them on.
However, if the machine isn't being adequately cooled, ie all the fans are working, there's enough fans and air flow to cool the components, etc., then it will do more harm to the machine the longer it runs.
From the sounds of your specific problems, it seems like a memory problem, I've had very similar symptoms before that were solved by pulling out what proved to be a bad RAM stick. But it's odd that it corrected itself on it's own, and that makes it rather hard to test for.
It is possible that it was a thermal problem, maybe one of the fans was gummed up and causing overheating, and it's since worked itself out. You might try getting a can of air, taking the machine outside, and just giving all the fans and the power supply a thorough blowout, to work all the dust out. Have you noticed any unusual sounds from the machine? Fan noise that seemed jsut a bit off, or quieter or louder than usual?
It can also, on rare occasions, happen that circuits essentially experience a "calamari effect", where the initial thermal conditions cause a failure in the circuit, but as they continue, they sort of warm back into place, so to speak.
but even there, that speaks to a heat problem that will doubtless cause mroe problems down the road, so best to get it checked out.