Pay Attention to the BGP state and table version

R1#sho ip bgp neighbors
BGP neighbor is 2.2.2.2, remote AS 200, external link
BGP version 4, remote router ID 2.2.2.2
BGP state = Established, up for 00:05:31
Last read 00:00:31, last write 00:00:31, hold time is 180, keepalive interval is 60 seconds
Neighbor capabilities:
Route refresh: advertised and received(old & new)
Address family IPv4 Unicast: advertised and received
Message statistics:
InQ depth is 0
OutQ depth is 0
Sent Rcvd
Opens: 1 1
Notifications: 0 0
Updates: 1 1
Keepalives: 7 7
Route Refresh: 0 0
Total: 9 9
Default minimum time between advertisement runs is 30 seconds

For address family: IPv4 Unicast
BGP table version 3, neighbor version 3/0
Output queue size : 0
Index 1, Offset 0, Mask 0x2
1 update-group member
Sent Rcvd
Prefix activity: ---- ----
Prefixes Current: 1 1 (Consumes 52 bytes)
Prefixes Total: 1 1
Implicit Withdraw: 0 0
Explicit Withdraw: 0 0
Used as bestpath: n/a 1
Used as multipath: n/a 0

Outbound Inbound
Local Policy Denied Prefixes: -------- -------
Bestpath from this peer: 1 n/a
Total: 1 0
Number of NLRIs in the update sent: max 1, min 1

Connections established 1; dropped 0
Last reset never
External BGP neighbor may be up to 2 hops away.
Connection state is ESTAB, I/O status: 1, unread input bytes: 0
Connection is ECN Disabled, Mininum incoming TTL 0, Outgoing TTL 2
Local host: 1.1.1.1, Local port: 15809
Foreign host: 2.2.2.2, Foreign port: 179

Enqueued packets for retransmit: 0, input: 0 mis-ordered: 0 (0 bytes)

Event Timers (current time is 0x5E5FC):
Timer Starts Wakeups Next
Retrans 14 5 0x0
TimeWait 0 0 0x0
AckHold 6 4 0x0
SendWnd 0 0 0x0
KeepAlive 0 0 0x0
GiveUp 0 0 0x0
PmtuAger 0 0 0x0
DeadWait 0 0 0x0

iss: 2209578516 snduna: 2209578745 sndnxt: 2209578745 sndwnd: 16156
irs: 2545650298 rcvnxt: 2545650527 rcvwnd: 16156 delrcvwnd: 228

SRTT: 197 ms, RTTO: 984 ms, RTV: 787 ms, KRTT: 0 ms
minRTT: 72 ms, maxRTT: 300 ms, ACK hold: 200 ms
Flags: active open, nagle, md5
IP Precedence value : 6

Datagrams (max data segment is 516 bytes):
Rcvd: 12 (out of order: 0), with data: 6, total data bytes: 228
Sent: 15 (retransmit: 5, fastretransmit: 0, partialack: 0, Second Congestion: 0), with data: 9, total data bytes: 228
R1#

The above is an example of "show ip bgp neighbors". Anything other than state established indicates that peers are not up. You should also note that BGP is version 4, the remote router ID (highest IP address on that box or the highest loopback interface in case it exists) and the table version (this is the state of the table. Any time new information comes in, the table will increase the version and a version that keeps incrementing indicates that some route is flapping causing routes to keep getting updated).