I lost my internet about 2 weeks ago for a few days, and I was playing Minecraft offline. I went to switch to a different profile on the launcher, and it logged me out for verification or something. I click 'play' and it says "We couldn't log you back in as (insert username). Please try to log in again.". I cannot access Minecraft at all at that point. Closing out the launcher doesn't do anything, can't swap profiles or even get past the login page for the launcher. This is not the first time it's happened, either. I only found out what caused it those few days without my internet entirely, rather than a short down-time.

It has something to do with the launcher_profiles.JSON recognizing profiles that you've played on with the last Mojang account to have logged in. Or it has to do with the launcher reading the .JSON incorrectly. You would think that if you just loaded Minecraft on all your profiles before losing internet connectivity, this wouldn't happen. However, it still happens regardless of that.

Test it yourself in launcher version 1.1.2 to 1.2.1 (haven't tested/had it happen any earlier than launcher version 1.1.2). Just modify/delete the launcher_profiles.JSON in .minecraft and then load a single profile in the new launcher, then take out your ethernet cable/whatever you use for internet. Once you try to swap profiles, you'll see what I mean.

Edit: Protip for anyone experiencing this problem: try to find your old launcher .exe. You may not be able to play 1.6 on it but at least you'll be able to play still if you lose your internet and this happens.