It is best to use proper Rosin based rework flux gel as this will aid with the heat transfer to the balls much more efficiently and last the soldering process so you only have to do the job once.

BGA rework should be done with rework flux paste, which is designed to stay active and will remain in place through the full range of reflow processes experienced during rework operations.

In addition, rework flux paste is tacky and will hold components in position the same way as solder paste.

All the major brands have a BGA Rework specific tacky flux formulation. I would start with the vendor you currently purchase your flux and solder paste from. This will ensure that your tacky flux is compatable with what you are currently using.

A flux with a good oxidation barrier (that protects molten solder from oxidizing for as long as possible) will do the job - typically no-clean rosin-based fluxes have a better oxidation barrier than water-wash fluxes.

The oxidation barrier in the flux is crucial towards eliminating head-in-pillow as well.

The key phrase in the question is "under prolonged heating".

In principle, the same flux or flux type as was used for reflow should be fine for rework. However, care must be taken to ensure that the flux is not overheated.The rework thermal cycle should be as close as possible to the one that was used in the reflow ovenincluding ramp, preheat, peak temperature, time above liquidus and cool down.

Following this simple rule should resolve the problem.

For replacement or repair I would recommend they use a no-clean flux cream. It tends to stand up to the heat of rework.