Two things to try first:
1. Different USB port, ideally completely away from a 'stack' of ports on your motherboard or laptop. Each such stack is typically connected to a single hub on the host controller. Such hubs can become unreliable over time (as can the host controller), particularly for such purposes as maintained connections streaming data from external storage devices. If the same cable and camera works on a completely different stack or even a completely different computer, chances are that hub and/or host-controller for the USB port(s) in question are gradually becoming faulty.
2. If this doesn't alleviate your problem, try a different USB cable in conjunction with the aforementioned.
On my motherboard, a now 5-years old ASUS P7H55D-M EVO, the board itself has six ports at the rear. Two black USB 2.0 at the top, two red USB 2.0 with increased power output for charging devices if using the appropriate ASUS software, and two blue USB 3.0 ports at the bottom. It has three headers on the board for another 6 ports, on which I've 4 extra ports at the moment.
Of these, the following is the case for my particular situation:
The black ports positively-hate anything like a webcam, USB headphones/headset, wired or wireless keyboard EXCEPT my Logitech G13. They're the most reliable for my USB 2.0 external HDD enclosure, which requires two ports.
The read ports positively hate external hard-drives BUT are my most reliable for my Yi and an external card reader. They're extremely temperamental with my G13 and will frequently require I reset the hub they're on for it to become active after boot/resuming from sleep.
The blue USB 3.0 ports hate my G700 mouse's charging cable and will more often than not simply not acknowledge there's something there. It's highly unreliable for card readers, external HDDs (will let them work, but they'll often disconnect arbitrarily), hates keyboards including the G13, and doesn't want to cooperate with webcams.
The 4 ports down below are my most reliable for my webcam, are unreliable for my Yi, don't acknowledge the existence of my card reader and require a reset of their hub once in a while for the G13. They work with USB headsets fine.
tl;dr moral of the story: USB is fickle and your problems may well be no more than a faulty hub or host controller on your laptop/motherboard.