Internet Connectivity Icon Only Displayed Sporadically

I am running Windows XP and I have a D-Link router, using a broadband cable
modem. My question is; Usually and unfortunately and sporadically, their are
two icons on my taking bar, in the lower right hand corner of my screen. One
indicates "Local Area Network" and the other indicates Internet
Connectivity. The Internet Connectivity icon seems to only be displayed
sporadically. I have checked Control Panel~Network Connections and I see
only the "Local Area Network" item. The Internet Connectivity item is only
there when it is displayed on the task bar. It does not seem to impact
connectivity for the internet and for E mail.

Why does this happen? How and what must I do for this feature to be there
all of the time and function dependently?