Determining if your problem is related to your network is not that difficult. You can try multiple file transfers and use special programs that will test the connectivity between two or more points, helping you rule out this possibility.
If your problem lies only on the e-mail service, then you should clearly look from your firewall toward your ISP. It could be possible that your Internet line is full during the day, making everything else seem slow, or there might be a problem with the e-mail server you are connecting to.
As you can understand, there are many possibilities why this problem is occurring and it must be broken into small pieces to be dealt with.
Summing up, start with your local network, ensure the network is running smoothly with no errors reported by the switches and double check your configuration. Then look at the Internet services (e.g., DNS and anything else you might use). Lastly, check your Internet connection -- is it being over-utilized during the day? If not, is your ISP experiencing any problems?
I'm certain that something from all the above will provide you an indication where the problem might be.
Dig Deeper on Network management and monitoring
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