I would like to state an additional observation made by me about the behaviour of WLM in my system. As mentioned in my OP, I started using my new Windows 7 laptop only six days ago. So, it is only now that I have firmed up this observation.
First, let me say that WLM remains online in my laptop always. I never make it offline.
Now, about the observation. In the morning, after I boot my laptop and start WLM, some mails from my corporate IMAP server downloads into my WLM. At that time, there is a popup notification and sound. Thereafter, when further new mails come into my inbox, there is no popup notification or sound.
Today, after some time, I removed the network cable from my laptop, and after few minutes connected the network cable back to my laptop once again. When new mails came in after this cable re-connection, again there was popup notification and sound. But, after that, no more notification / sound when further new mails came in.
Summary of my observation : I get a popup notification and sound, only after booting my laptop, OR after disconnecting / re-connecting my network cable, and not at any other time when new mails are getting downloaded.