When attempting to update Discord with BullGuard's protections active, Discord will go into an infinite loop of searching for update, downloading update, and installing update in <1 sec increments. Temporarily disabling the anti virus and firewall protections allow Discord to update normally. Adding exceptions for Discord to the firewall and anti virus does not allow Discord to update normally.
Doing a Google search as to why Discord was doing this pointed me to a handful of forum posts on the first page of Google that pointed to BullGuard's protections being the problem, and sure enough, it was. It is apparently a common enough issue that BullGuard was named specifically as to the cause of the exact issue I described with Discord's updating loop.
BullGuard version as of writing: 21.0.388.1