GPU struggles only in the primary PCIe slot. Is this a motherboard issue?
If the GPU is using legacy interrupts for some reason, it may be suffering from high latency while the CPU is busy handling other interrupt handlers for that IRQ.
Your motherboard's user manual specifies that the PCIE x16_1 slot (the top one) shares IRQ assignments with the internal graphics, HD Audio, USB 2.0 (EHCI), and PCI 2 slot.
Modern motherboards with PCIe are supposed to be exposing interrupts over a newer system, so the existence of this chart in your user manual is unexpected.
The PCIE x16_2 has its own IRQ assignment, so it does not have to compete with any other components to raise an interrupt request. If the GPU performs better in that slot, this may be the explanation for better performance.
However, that slot is only PCIe 8x.
With PCIe 8x you might lose performance in some programs that are bandwidth heavy. That won't have a significant impact on FPS for most games though.
There should be no issues running your GPU in the second slot. That said, it's important to note that running any GPU in that means it only receives 8 PCIe lanes of bandwidth, instead of the full 16 it would get in the primary slot. However, since your GTX 960 is a relatively old and slow card, it's unlikely that having access to only half the lanes will bottleneck it in any way.
Should you be willing to invest the time and effort in actually tracking down and solving the issue so you can put the card back in the first slot (wouldn't blame you if you aren't!), be prepared to do some digging:
If your system has only recently started having problems, then assuming you haven't changed anything (i.e. updated BIOS or drivers), it is possible the motherboard is physically faulty. On the other hand, if you haven't updated the motherboard's BIOS or its drivers (especially for chipset and/or onboard sound), then now might be the time to do so.
It's also quite possible that a Windows update changed something thus causing this issue. If you can remember approximately when the issue started happening, it might be useful to review your machine's Windows Update history for updates around that time. As a last resort, if you have a spare SSD/HDD and some time, you can install a fresh copy of Windows on that drive then put the GPU back in the primary slot and see if it performs as it should. If so, you know something is broken in your current Windows install, and a reinstall will likely fix it.