If I am reading your post correctly you said that you are getting the "SNMPTrap::::::Connection Limit Exceeded Connection Limit Exceeded" alert in your monitoring console.
I don't believe that this is a problem with your BigIP, it might be a limitation of your monitoring console getting flooded with SNMP Traps from the BigIP. The notifications should be proportional to the amount of incidents that the BigIP is trying to notify you about (in this case it could be the traffic rejected by a disabled VIP or a combination with other events).
I've gotten the same type of Packet rejected messages that you are getting in your LTM Log, they are just informational. They only impact they have is increasing your LTM Log File Size. If you want to get rid of the alerts you can enable the VIP and apply a traffic drop iRule on it.