Update: forcing the mainboard to use PCI-E 1.0 speed seems to solve the issue.
This can be done in the BIOS utility -> Advanced -> PCH Configuration -> PCI Express Configuration -> PCIe Speed: set from "Auto" to "Gen1"
This has bene suggested by one of the posters here, in relation with Nvidia GPUs suffering from a similar error in X-99 chipset based mainboards:
While downgrading PCIe is a workaround, it's still an issue waiting for a proper solution.