SNMP outputs are fine :
bgp4V2PeerAdminStatus.1.2.16.42.0.191.64.0.0.0.0.0.0.0.0.0.0.0.2.2.16.42.0.191.64.0.0.0.0.0.0.0.0.0.0.0.5 = halted bgp4V2PeerAdminStatus.1.2.16.42.0.191.64.0.0.0.0.0.0.0.0.0.0.0.2.2.16.42.0.191.64.0.0.0.0.0.0.0.0.0.0.0.6 = halted
(I haven't looked enough into the alerting subsystem, so playing this by ear)
You are testing on bgpPeerAdminStatus notequals stop.
Your snmp output is for bgpv4V2PeerAdminStatus, but lets assume it's being caught correctly and passed over to the other naming... You still need to change your test to be notequals halted (as the BGP4V2-MIB only has 'halted' and 'running' as the states).
Try making a new alert checker with the test condition set to
bgpv4V2PeerAdminStatus notequals halted or bgpPeerAdminStatus notequals halted
But you'll probably also need to set the right peer state
bgp4V2PeerState notequals established
Michael