It is only natural that if nobody else is experiencing similar issues, but you are, then the problem lies with the computer. Either a hardware / software / settings issue.
However, from what it sounds like, it seems probable that it may be a heat issue. This is usually the case when the problem seem to occur only after some time. Assuming if it is, the resolution is figure a way to cool your CPU more, or consider running on lower settings for in game graphics.
I am not sure about the newer Activision games today, and I am unsure if you are familiar with how Blizzard games work. So what happens is that the games usually have a very wide range in terms of how poor or excellent you can set the graphics settings to. I think WoW is a very good example of it.
I can still play WoW with my 7 year old laptop (which I did in the past), but I probably will not be able to set my vision limit to the max. Though I am able to set it far enough that it seems just natural like any other MMORPG.
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So to tie it back, it is a technical issue, but not something that Activision needs to fix. Plus the fact that they have already announced that they are scaling back on SC2 matters. So whatever issues that players are facing, unless it is as major as preventing every single one from playing, it is going to be as it is.