Hello,
I'm sorry but I do no see any BGP going down with these logs:
Jun 1 14:45:54 DEVICE-re0 rpd[1541]: %DAEMON-4: bgp_adv_main_update:8762: NOTIFICATION sent to NEIGHBOR-1 (Internal AS MY AS): code 6 (Cease) subcode 6 (Other Configuration Change), Reason: Configuration change - VPN table advertise
This log is a Notification sent to the neighbor.
Jun 1 14:45:54 DEVICE-re0 rpd[1541]: %DAEMON-4: bgp_adv_main_update:8762: NOTIFICATION sent to NEIGHBOR-2 (Internal AS MY AS): code 6 (Cease) subcode 6 (Other Configuration Change), Reason: Configuration change - VPN table advertise
This log says there's an BGP advertise, that's normal as the routing-table has changed, It has to update neighbors
Jun 1 14:45:54 DEVICE-re0 rpd[1541]: %DAEMON-4: bgp_set_peer_if: BGP peer NEIGHBOR-3 (External AS ISP AS) interface not found. Leaving peer idled
This message it's a litle more to worry about, it's seems when the new peer was added, there weren't interface for this neighbor, BGP status went to idle.
Base on this logs, I do not see any neighbor going down, I do not see BGP DOWN neighbor message.
Are you sure the new neigbor comes up?
Do you see the timers for old BGP neighbors reseted?
Regards,
LordofOceans 