Unfortunately if you've severely 'over-cooked' a joint, the solder can dissolve significant concentrations of additional copper from the pad and/or lead. This increases the melting point and shifts it away from a eutectic composition. Wicking such a joint without fully melting it makes the situation worse as it removes the near eutectic composition liquid leaving the solid crystals with higher copper concentration further increasing the melting point. Combined with poor thermal transfer due to a dirty joint surface, inadequate iron, or poorly tinned bit, and with large copper planes on inner layers without thermal reliefs, the result can be nearly impossible to rework successfully.
Generally if a joint isn't melting freely, you need to stop and figure it out rather than carrying on and cooking it. Clean and tin your bit, apply fresh solder + flux to get better thermal transfer, and it may come good, but if it doesn't you are either going to need to preheat the board to 100 deg C, or use
ChipQuik or other similar low melting point alloy to dilute the solder in the joint and lower its melting point sufficiently.
N.B. there are different ChipQuik alloys for SnPb solders and RoHS (lead free) primarily Sn based solders - get the right one for the work you are doing!
@Shock: Photo attached with one paper disk removed to show how its punched. There are currently seven disks in the wiper stack. Sorry about the poor photo quality.
@David Hess: Yes, tip movement can be a problem with delicate pads. Silicone tubing on the tip helps as it cushions the harder PTFE tip, but if its extremely delicate, a manual sucker isn't the best choice. You can try a squeezy bulb sucker but I've never been impressed by the level of suction they deliver.