No need to worrried about that, if you have concern related to BGP you need to look at BGP process.
show ip bgp summary
TCP handshake always happends all the time its life time process.
L0ok at RFC reference :
A connection progresses through a series of states during its
lifetime. The states are: LISTEN, SYN-SENT, SYN-RECEIVED,
ESTABLISHED, FIN-WAIT-1, FIN-WAIT-2, CLOSE-WAIT, CLOSING, LAST-ACK,
TIME-WAIT, and the fictional state CLOSED. CLOSED is fictional
because it represents the state when there is no TCB, and therefore,
no connection. Briefly the meanings of the states are:
LISTEN - represents waiting for a connection request from any remote
TCP and port.
SYN-SENT - represents waiting for a matching connection request
after having sent a connection request.
SYN-RECEIVED - represents waiting for a confirming connection
request acknowledgment after having both received and sent a
connection request.
ESTABLISHED - represents an open connection, data received can be
delivered to the user. The normal state for the data transfer phase
of the connection.
FIN-WAIT-1 - represents waiting for a connection termination request
from the remote TCP, or an acknowledgment of the connection
termination request previously sent.
FIN-WAIT-2 - represents waiting for a connection termination request
from the remote TCP.
CLOSE-WAIT - represents waiting for a connection termination request
from the local user.
CLOSING - represents waiting for a connection termination request
acknowledgment from the remote TCP.
LAST-ACK - represents waiting for an acknowledgment of the
connection termination request previously sent to the remote TCP
(which includes an acknowledgment of its connection termination
request).
TIME-WAIT - represents waiting for enough time to pass to be sure
the remote TCP received the acknowledgment of its connection
termination request.
CLOSED - represents no connection state at all.
