Nowadays, I do not visit my Stack Exchange site frequently. Until now, I know that if I obtained some badge once, then it is permanent. This is one difference from reputation. Today, I suspect that my number of badges decreased. My question is: Can we lose our badges?
Yes, that's possible, but in practice only for one class of badges: tag badges. Each night your tag scores are recalculated; if you fail to meet the criteria (because of downvotes or retaggings) you'll lose the badge.
Unlike most other badges, tag badges are revoked immediately if you ever cease to meet their criteria, which can happen if your answers are downvoted, deleted, or converted to community wiki, if the tag is removed from questions that you've answered, or if the tag becomes ineligible for badges because it's no longer used on 100+ questions.
Normal badges can't be lost, except for egregious cases of vote fraud when the Community Team may decide to manually revoke unfairly earned badges.