Like the other answer, I too re-inforced a NEW cable, as a pre-emptive measure.
I experimented a little with the heat shrink tubing and superglue method, but supergluing the smaller heat shrink tube (which has to be slit in order to put on the cable) is messy, and prone to failure after applying the necessary heat to shrink it tight on the cable.
Better, cheaper, and far easier is to simply use high quality 3/4" BLACK ELECTRICAL TAPE to reinforce that (Nook Color/Tablet) end of the cable, in three steps, as follows:
Wrap the tape tightly around the cable itself, on the area closest to the connector, until it is the same diameter as that first (round) stage of the connector. Cut the tape.
Next wrap more tape over that area, close as possible to the larger (square) part of the connector, so that it covers both the previous tape wrap plus the smaller round (flange) part of the connector. Wrap tightly until it is about level or possibly a little higher than the square part of the connector. Cut the tape.
Next wrap more tape around that last wrap of tape plus part of the square connector, say with the edge right at the "n" LED, with about 3 turns maximum. Cut the tape. All done.
Advantages to this method include NOT subjecting the cable end to heat high enough to shrink the heat tubing (and possibly causing other damage). Also you don't need any other equipment or materials besides 3/4" electrical tape and scissors. Wrapping in 3 separate "level" sections keeps the tape from wrinkling, and if wrapped tightly, looks quite neat when done.
RECOMMENDATION: Wrap in the SAME DIRECTION for each of the 3 sections, and cut the tape such that tape sections end on the opposite side of the connector's "n" LED.