OS X repeatedly stops syncing contacts and calendar with Gmail

For what feels like forever (but is probably only a year or two), OS X constantly ‘loses’ my Gmail password. This is particularly annoying, because I use two-factor-authentication with my Google account, and have to go generate a new password every time I see this bug:

Even worse, I don't know there's any problem until I actually open the Contacts application (a thing I never do). I'll get text messages on my Mac, and wonder who the hell's messaging me, because it'll show up as a phone-number; meanwhile, I created a new contact for that person months ago on my iPhone, and it turns out Google hasn't synced to my computer in that entire time.

I clear all the Google/Gmail entries out of my keychain, generate a new one-use password with Google, and put it in OS X, every time I see this. It just happens again a couple months later.

Does anybody know what could be causing this?