I don't know the specific details of the logic board you're working with, but in general multi-layer circuit boards are often difficult to desolder components because the many copper layers within the board can too easily conduct the heat away from the area you're trying to heat, especially if you're using a low wattage soldering iron. in any case you need to be careful about overheating the board and possibly delaminating nearby traces.
are you using a [http://en.wikipedia.org/wiki/Desoldering_pump|solder-sucker] or [http://en.wikipedia.org/wiki/Solder_wick|solder wick] in addition to heating with an iron? those may help