a) In chess, it is considered that the side who has a clear disadvantage does not offer the draw. (The other side knows you want a draw)
b) After a draw is declined, the same player usually does not offer the draw again (You got your offer declined, your opponent will make the offer if he changes his mind).
2. It's a draw
After 50 moves of no captures or pawnmoves you are able to claim a draw. This is called the 50 moves rule
-edit-
Some exceptions:
A far higher rated player (say 400 points) might once offer a draw because his opponent "might" fear the ratingdifference, and both might want a draw.
When down in material but serious up in time (lets say opponent has only 20 seconds left) you might want to offer the draw, but only once!