Vernier is actually right. If your gamertag is disconnected from Live, then you continue to acquire achievements while offline, those achievements will be added to your game progress when you come back online. There is no "Achievement Unlocked" icon at the bottom of the screen as soon as you connect online. It simply just slips those achievements into the games you played.
This is NOT you issue however. When you remove the account (using it on a different console for example) then recover it, there is no recovering the achievements earned offline. This is because there is no record either on your hard drive, Memory Unit, or USB stick that, the achievement was unlocked on that particular account. The system sees it as unlocking the achievement on an offline profile that happens to have the same name as your gamertag.
I learnt this the hard way after losing about 400gs in Dragon's Age: Origins. You have to play it again. Moral of the story is, use the "Recover Gamertag" feature SPARINGLY. Move data and gamertags between consoles using a USB stick. That way the gamertag is kept together with it's saved games.