Like wa8yxm asked - what type of connector? For the common 7 pin Bargman, the cover on the male (vehicle) end has a tab which should lock the trailer end in place when it's fully seated.
Maybe the tab is broken, maybe the spring on the cover is broken, maybe there's gunk in either connector which is keeping them from fully mating.
(the gender is defined by the contacts - 6 of the 7 are male on the vehicle side, so that's considered the male end, although it's less ambiguous and confusing just to refer to vehicle/trailer)
