I've had very good luck reusing fittings.
There are a few things to keep in mind.
The first is yourself. It's quite idiotic to try to save a $0.75 fitting if you damage yourself in the process.
You should have safety glasses, long sleeve cotton shirt, cotton gloves and a cotton towel for this. Have your flux, solder, sandcloth and fitting brushes as well. If you don't have a fire extinguisher also, leave now.
Heated flux burns easily and can be hard to control, even for the best of us. Plus it'll give you some pretty mean welts if you don't watch out.
Generally, you want to keep the fitting 'wet'. This means keeping some flux on the fitting while heating the solder. This will help in liquifying the solder without overheating the fitting.
Female joints can be desoldered by heating the fluxed fitting and using a fitting brush to remove solder. It's a process that usually takes a few heat cycles to accomplish.
To remove solder from an end of pipe, flux, heat and wipe with the towel. Once cool, sand before resoldering.
All this being said, I wouldn't recommend this on any fitting that's already in place. It is far too easy to compromise the existing joint(s) in the effort to save the bad.