A healthy coral can often survive in less than excellent water conditions(not saying yours are)
An unhealthy leather will rarely recover unless water IS excellent(not saying yours is not)
Algae growth on the "stump" usually indicates high nitrates and/or low flow.
The polyps are extending from the cap ...are they opening?
Is the base of the leather securely attached to a rock?
A "stump" that is deflated, hard and has a woody feel(feels like an old tree branch) and whose polyps barely entend or do not fully entend throughout the cap is a sign that it needs help or will most certainly be on its way out.
Without more info it is tough to say what is going on for sure. To help a little I would suggest (providing it is attached securely to a good base) cleaning all the algae off, moving it to the highest flow area in the tank(not directly in front of a powerhead
) and simply leaving it alone for several weeks. As long as it does not show signs of melting I would not frag it. Try to keep the salinity of the tank as stable as possible and water quality as good as you can (not that it isn't already). It only takes a few days(or less) for a leather to decline in health but can take weeks or months for it to recover. With a little patients yours will problably recover in time but these changes do not happen quicky ...especially if you started with a less than healthy piece.
SiF