Looking at this:
https://bugs.launchpad.net/ubuntu/+source/linux-lts-utopic/+bug/1492146
and this:
https://lists.ubuntu.com/archives/kernel-team/2015-June/058586.html

I think it may be a kernel issue and ClearOS hasn't caught up to those yet?

Thank you both for your replies, I'll try to find the thread mentioning the pcie_aspm and see that it was for. I am using 7.2, and I have installed Intel's latest driver. Unfortunately, it did not resolve the issue. Also, just as a note, it happens much more frequently when the NIC is receiving a heavy amount of traffic. The very odd thing is again that it only happens with the second nic, not the first. I have updated the bios.

Additionally, I have seen others having similar issues on other distributions, (i.e. Ubuntu) and they have fixed it by upgrading to a newer kernel, 4.4 for instance. Do I have that option? If so, how would I do that?

If I remember rightly there was a problem discussed on the CentOS mailing list recently re. a SUPERMICRO motherboard and its on-board Intel 82574L NIC as implemented by SuperMicro... The solution was to add "pcie_aspm=off" to the kernel parameters. Not sure if this applies to your board, but worth a try at least...

I am assuming you are using ClearOS 7.2 and it uses the native driver. ElRepo no longer maintain an igb driver as the stock one has been virtually up to date. The kernel driver, 5.2.15, is a little behind Intel now, who have released 5.3.5.4. Unfortunately the changelog on Intel's site is somewhat lacking. You could try compiling their later driver but be aware that you may have to recompile it every time the kernel upgrades.

What concerns me is that I suspect it may not be a driver issue. I use a standalone i210 card and have no problems with it and the native driver. I wonder if it is a Supermicro issue. Do you have the latest BIOS installed?