I was just searching for this problem as my icon is also not appearing regularly these days. I also use Windows 7 home 64 bit and Avast free. It seems to be a semi-random issue but I must say I was annoyed enough today to log in here and mention it at the very least. Tray notification is checked, windows notification is set to always display icon. I've soft booted, I've hard booted. Done this dance many times, sometimes the icon comes back, sometimes it doesn't. I like the product and have used it on one computer or another since I can't even remember.. 10 years? more? But please, please... the darn tray icon. I'm not doing any sorts of deep system manipulating, I'm browsing the internet, watching videos and listening to music. I'm not installing, uninstalling, restoring, wiping, swapping hardware.. just nothing but the most mild end user stuff.
This issue happened on my now defunct laptop too. It also ran windows 7, but I guess since I can't delve into anything on it now (hard disk failed) we can't explore anything about it. But I assure you, it would randomly display or not display the Avast icon.