If you have bought these young rabbits (rather than bred them yourself), it is possible you don’t actually know the breed, or at least the parentage of the rabbits. If they are lop-eared rabbits (such as the Holland Lop), then their ears start to droop as they get older – they are not born like this. If they are lop-eared, each ear will droop independently and on each individual at a different time, but generally at about 5 weeks, and fully "lopped" by about 10 weeks. If the parentage is mixed, it is possible that only 1 or 2 of the rabbits’ ears will droop, or that only one ear will droop.

In addition, it is not unusual at all for any rabbit to have one droopy ear, probably as a result of a weaker base that cannot support the full weight of the ear. This is unlikely to cause any health problems and often it is considered a very cute characteristic!