I'm not sure if this is the system tray icon (bottom right) or the desktop icon, which although useful isn't an essential part of your avast program.
This relates to the avast ' a ' icon in the system tray. If this is continually happening (icon gone) it is almost certainly another security program at work.
As a temporary measure until this is resolved you can create a desktop shortcut for this file C:\Program Files\Alwil Software\Avast4\ashDisp.exe (the avast icon and interface to the providers). Right click on the file and select Send To, Desktop (create shortcut). You will need to run this after each boot until the problem is resolved.
What other security based software do you have that might block new startup entries, e.g. Spybot S&D (TeaTimer), AdAware (AdWatch), SpySweeper, Spyware Doctor (StartUpGuard), PrevX, WinPatrol, ProcessGuard, etc. ?