I have had a very similar problem a couple of times in the past with my Samsung tablet. It was always software-related, and never the cable or charger (I have two original Samsung chargers for that tablet, and both had the same problem, as did various cables. For me, it would not charge past 50%.
The first time, I let the battery discharge all the way until the tablet went into severe battery-saving mode, and I let it go as long as I could until I lost patience. I then charged it up, and it worked OK after that. It happened again, it seemed, a few months later. This time, I unplugged the charger,turned off the power, then plugged it back in and it charged OK.
Samsung phones are often picky about chargers. I've found that some will not work at all with my Samsung tablet, but will work with my LG G2 and my wife's iphone, while others work with it, with my LG, and with my wife's iphone. I never really figured out exactly why. But as with all chargers, sometimes they will work, but at only .5 amp if you don't have the right match, or a special charge-only cable. So, if you have such a charger, it might not be able to keep up with the discharge.
I worked in electronics repair, testing, and design for about 15 years, so I have a good understanding of the basics, and troubleshooting. People who suggest special short, thick, whatever cables are simply not very knowledgeable, or repeating misinformation from others who are just guessing out of partial knowledge. For the amount of current going through the cable, and the difference in resistance for different types of cable, the loss is negligible. The only time a cable will make a difference is if the connector is damaged, or it is wired in a nonstandard way internally. Of course, a cheap cable can have a wire break, but that has nothing to do with size of cable.
Also, if you're not careful, the connector on the phone can be damaged, or have foreign matter caught inside, or some obstruction keeping it from making a good connection. The micro-USB connection is not the most robust way of making a connection, which is probably why they are creating a new standard.