I suggest waiting for the problems to occur and then checking the Event Viewer logs for relevant messages. (Hit Windows Key + R then type eventvwr.msc [Enter] - check Application and System logs).
I had a similar problem a couple years ago and it was fixed by a registry tweak, unfortunately I do not recall exactly what it was but I found a couple links based on my recollection:
The one I am really leaning toward (I think the one that solved my problem) is the second half of the first link:
Change value to 3 and then reboot.
I do not think my problem was exactly yours, but I rmember the file shares failing after a period of time and this fixing it. I have checked the machine that I think was the culprit at the time and it has the value 3, which is not the default so I know I changed that one for some reason. I no longer use that machine as a file server, now have a NAS doing that job, so I’m not 100% sure, but I think so.
That IRPStackSize really rings a bell with me but looking at the PC in question, I do not see that I ever added that key, so I could just be completely insane.
Your comment about Win7 Home vs Pro makes me think of back in XP when there was simple file sharing vs advanced file sharing, and I wonder if maybe something similar still exists in Win7 and perhaps the difference accounts for the difference you are experiencing between the two OSs.
In any case, even if my fix is wrong for your your problem, checking Windows event logs would be the best place to start. If you can identify a relevant error message or messages you’ll at least know what to search for in pursuit of a solution.