As shown in the figure, R1 is in AS1, R2, R3, R4 are in a large AS100 (R2, R3 are in AS23, R4 is in AS4), and 5 is in AS5. 
The loopback between R4 and R5 uses EIGRP to establish a neighbor relationship, and R4 and R5 establish an EBGP relationship. The neighbor relationship is sometimes DOWN and sometimes UP.
Solution--BGP Backdoor
R4#
Apr 12 20:47:46.939: %BGP -5-ADJCHANGE: neighbor 5.5.5.5 Down Peer closed the session
R4#
Apr 12 20:47:49.707: %BGP-5-ADJCHANGE: neighbor 5.5.5.5 Up
R4#
Apr 12 20:47:46.263: %BGP-5 -ADJCHANGE: neighbor 4.4.4.4 Down BGP Notification sent
R5#
Apr 12 20:47:46.263: %BGP-3-NOTIFICATION: sent to neighbor 4.4.4.4 4/0 (hold time expired) 0 bytes
R5#
*Apr 12 20 :47:49.283: %BGP-5-ADJCHANGE: neighbor 4.4.4.4 Up
R5#
R4#show run | s bgp
router bgp 23
no synchronization
bgp router-id 4.4.4.4
bgp log-neighbor-changes
network 4.4.4.4 mask 255.255.255.255
neighbor 2.2.2.2 remote-as 23
neighbor 2.2.2.2 update-source Loopback0
neighbor 2.2.2.2 next-hop-self
neighbor 3.3.3.3 remote-as 23
neighbor 3.3.3.3 update-source Loopback0
neighbor 3.3.3.3 next-hop-self
neighbor 5.5.5.5 remote-as 5
neighbor 5.5.5.5 ebgp-multihop 255
neighbor 5.5.5.5 update-source Loopback0
no auto-summary
R4#show run | s eigrp
router eigrp 23
network 4.4.4.4 0.0.0.0
network 24.1.1.4 0.0.0.0
network 34.1.1.4 0.0.0.0
network 45.1.1.4 0.0.0.0
network 45.0.0.0
no auto-summary
R5#show run | s bgp
router bgp 5
no synchronization
bgp log-neighbor-changes
network 5.5.5.5 mask 255.255.255.255
neighbor 4.4.4.4 remote-as 23
neighbor 4.4.4.4 ebgp-multihop 255
neighbor 4.4.4.4 update-source Loopback0
no auto-summary
R5#show run | s ei
R5#show run | s eigr
R5#show run | s eigrp
router eigrp 23
network 5.5.5.5 0.0.0.0
network 45.1.1.5 0.0.0.0
no auto-summary
R5#
solution
R4#show run | s bgp
router bgp 23
no synchronization
bgp router-id 4.4.4.4
bgp log-neighbor-changes
network 5.5.5.5 mask 255.255.255.255 backdoor
neighbor 2.2.2.2 remote-as 23
neighbor 2.2.2.2 update-source Loopback0
neighbor 2.2.2.2 next-hop-self
neighbor 3.3.3.3 remote-as 23
neighbor 3.3.3.3 update-source Loopback0
neighbor 3.3.3.3 next-hop-self
neighbor 5.5.5.5 remote-as 5
neighbor 5.5.5.5 ebgp-multihop 255
neighbor 5.5.5.5 update-source Loopback0
no auto-summary
R4#show run | s bgp
router bgp 23
no synchronization
bgp router-id 4.4.4.4
bgp log-neighbor-changes
network 5.5.5.5 mask 255.255.255.255 backdoor
neighbor 2.2.2.2 remote-as 23
neighbor 2.2.2.2 update-source Loopback0
neighbor 2.2.2.2 next-hop-self
neighbor 3.3.3.3 remote-as 23
neighbor 3.3.3.3 update-source Loopback0
neighbor 3.3.3.3 next-hop-self
neighbor 5.5.5.5 remote-as 5
neighbor 5.5.5.5 ebgp-multihop 255
neighbor 5.5.5.5 update-source Loopback0
no auto-summary