If you are having trouble maintaining eye contact with people then it is a sign that you are having trouble managing tension.  I used to struggle with this big time.  I would always look away if a girl caught me looking and I would break eye contact first with men.

Try this exercise: when you are out in public, make eye contact with everyone and hold it.  Make them be the one to look away first.  Word of warning – if you do this to a man it can be misconstrued as aggression and that is obviously not what you’re going for.  So feel free to give him a head nod or gesture to acknowledge the connection as friendly rather then hostile.  As you get comfortable, start giving the women a sly smile or flirty look.  When you can master this, you’ll be in the top 1% of men who can attract a woman from across the room without saying a word.  Your eyes say everything.