It is a bit surprising given that there is easterly wind shear (on the decline) and marginal SSTs of 25 to 26C, but its also true that those conditions didn't stop Bertha when it came off the coast in roughly the same area (SSTs were about the same). This particular wave has maintained a tropical low center for about the past four days - its roughly located near 13N 13W at 21/00Z. The wave will exit the coast on Monday (not Tuesday) and has a chance to become a depression on Tuesday (per the UKMET, which is what I'm sure NHC was looking at). In general though, you are correct that many of them do fall apart when they first exit the west African coast. The MET develops it as a tropical cyclone at 15.7N which seems a bit too far to the north given its current location.
ED