The detectors have different sensitivity depending on the direction of the waves, so if a wave comes from a "bad" direction (perpendicular to both arms, e.g. directly from above), a particular detector might not detect anything, even if the wave is strong.
This is why (amongst many other reasons) it's important to have multiple detectors around the world (e.g LIGO has two locations in the US, you also have Virgo in Italy, and they do collaborate), this way you can assure in theory that you can "see" every wave, no matter which direction it's coming from.
(AFAIK).