lb::reselect fails to select another node

I'd say you need to open a Support case, then, especially if you've been struggling with this for several months without resolution.

An iRules workaround might be to manually re-select the other server, then bail out if both are non-responsive. I've had other customers implement similar logic successfully for other reasons, but it obviously won't scale well above 2 servers:

when CLIENT_ACCEPTED {
  set failed 0
}
when LB_FAILED {
  incr failed
  if {$failed > 1 }
    specify action if both servers failed
    reject
  } else {
     default case would match if no pool or server selected
    switch [LB::server addr] {
      1.1.1.1 { node 1.1.1.2 0 }
      1.1.1.2 { node 1.1.1.1 0 }
      default { reject }
    }
  }
}

The advantage of monitoring is that a monitor looks for an expected response, rather than just a SYN/ACK, to determine if the server is healthy enough to receive traffic.

HTH, and please let us know what you discover with Support.

/deb