Ask your Administrators who is the person receiving the BES Alerts. BES alerts are basically emails from the BES server when something happens or goes wrong. Sometimes it is a pain because I could receive many many useless emails about users being added or removed from the server over the course of normal Admin work (done by others as well as myself), but the key in these emails is to watch for things like SRP connection drops and "hung threads".
If these aren't even being looked, or in the least if the event logs on the BES server are not being monitored once and awhile, problems will go unnoticed.
So many small items could go wrong with a BES server, it takes some investigation, right from making sure the Server NIC is configured with the right duplex and speed of your switch (to avoid the possibility of repetitive renegotiation). We once were using an onboard "Nvidia" network card and it just wasn't cutting it. We moved to an onboard Intel NIC (4 onboard nics on this server) and things improved dramatically.
Goes to show you it could be anything. Start hunting