I hate to tell you that you need a larger tip and more heat, but as Mondak mentioned, that is exactly the problem. If you aren't experienced at soldering, my personal advice is to let a repair center do it. It's easy to damage a pcb with heat. But, if you're determined to do it yourself:
A typical professional setup uses a mechanical-vacuum desoldering station whose hollow tip runs to about 1300 degrees. That's about 700 degree hotter than the soldering iron to keep the extracted sodler liquid long enough to reach the capture tube.
You will probably do better with a rapid heatup using a iron around 65-80 watts having a chisel tip (on the left)
or a round tip cut on the bias to provide a flat surface to rapidly transfer the heat. Don't try it with a pointy tip (on the right), you 'll never get enough heat down to do anything because both the joint and the wick are sucking heat away from where you need it.
You might also consider a drop or two of liquid rosin flux on the wick.