Updated: February 6, 2016
The problem you are facing is as follows. You have a Windows 7 box, most likely a desktop, and you have a brand new external USB 3.0 hard disk, which is entirely powered using a cable. When you plug it into the computer, it's properly recognized, however it disconnects and then reconnects during sustained large file transfers. What now?
The bigger issue is that everything worked for a while, without any issues. And you can also successfully connect the hard disk using back USB ports on your motherboard. The problem only comes to bear when using the front ports. Anyhow, this is the long story short of your woes, and I'd like to give you a solution.
Deeper problem analysis
When facing an issue like this, you may believe you are facing a hardware problem, a firmware issue, bad drivers, motherboard incompatibility with new devices, faulty stuff, bad or dodgy cables, insufficient power, as well as other weird things. It is very easy to diverge and lose control. Which is why we need to take it step by step.
The very first thing you must ask: what has changed in your setup? The answer is, probably very little. In mine, just a set of Windows updates, so this means it's most likely a driver problem, or a conspiracy to wean you off Windows 7 of course. But let's not go there. Let's focus on the technical side of things.
Do you have a faulty disk and/or cable? Very easy to check, and you might need some help from friends here. Try multiple disks, multiple cables, multiple USB ports, back and front, multiple computers. Look for a common pattern that persists across all use cases.
In my scenario, the affected, brand new hard disk was working perfectly fine when connected to front USB ports on a second computer, also running Windows 7, and back ports of the same computer. This means we can discount any faults with the device or the cable, as well as any Windows 7 conspiracies. The problem seems to be the front ports on the relevant machine.
Now that I've helped you think and reason - known as component search in the statistical engineering parlance, which you might want to consider and embrace, now we need to figure out WHY the front ports are being dodgy.
The simple guess is power. If the device does not have sufficient power or is being managed in a shoddy manner, it may suspend at wrong times, which means it will disconnect and then reconnect, but also screw up your file transfers. To see whether this theory holds, you will need to change your power options:
Control Panel > Power Options > Change plan settings > Change advanced power settings. In the window that opens, scroll down to USB settings > USB selective suspend setting. Here, change the default value of Enabled to Disabled. Reconnect the hard disk and try to copy some files. Does it work? Good. No? Then my article didn't really help you.
For a whole bunch of guides on other weird problems of similar nature:
Windows 7 Samba errors
Windows 7 share access denied
Windows 10 & network sharing problem
Linux Mint KDE touchpad issues
There might be many other reasons why your hard disk is misbehaving, but you are most likely facing the same issue I had, and it comes down to power management. It is utterly annoying, especially if your setup did not change, and Microsoft bungled an update with some arcane and possibly arbitrary power setting change. I hate this kind of problems, because they are utterly unpredictable and unnecessary, and they may erode your confidence in your systems.
Always remember, if you practice sane computing like I do, you should always assume it is someone else's fault. As we have seen in a dozen other articles showcasing similar issues, it is indeed the vendor cramping your style and not the other way around. Well, I hope my little tutorial has helped. If not, I'd presume the device could be drawing too much power, and the front ports don't have sufficient voltage or current to sustain it. Other than that, we ought to conclude. Hopefully you've learned something useful today.