Firstly, is there any manufacturer support with that system? I'd go that route first
Secondly, make sure firmware is upgraded on EVERYTHING across the board, because this does sound like a firmware or buffer overflow issue where a device clears out after a reboot. Check the ISP/modem, Edge Device (I'm assuming a Fortinet Router), Switch, Phones, and even WAP if they're PoE. ANy one of those could be sending bad packets, have a firmware upgrade, or a NIC going bad that is causing this.
Then, after all of those are confirmed, run a packet capture with wireshark right after they start having the problem again (if it crops up, after the verification of upgrades across the board) and see what packets are dropping, or what errors persist on the network.