When David hears Natan's rebuke, he has only two words to say: "Chatati la-Hashem" – I have sinned against the Lord." Without a doubt, these words reflect enormous strength.
Other kings who were the objects of a prophet's rebuke responded in altogether different ways. Some kings seethed with rage and ordered that harm should be brought to the prophet; this was the response, for example, of Yerovam ben Nevat and Achazya. Others tried to evade responsibility – this was highly characteristic of Shaul, who time and time again tried to justify his actions. David, in contrast, recognizes his sin, is not angry with the prophet, and does not try to excuse his actions. This response was appreciated on high, and accordingly Natan informs David that his repentance was effective for the short term and saved him from death.
The Bat-Sheva episode was indeed a serious one-time fall of David, but it did not reflect his person as a whole. Against this fall stands the greatness of David's person as it was expressed on various occasions, and it may be concluded that David learned his lesson, and that the serious episode reflects the exception, rather than the rule – unlike Shaul, whose fall reflected an essential flaw in his leadership, and therefore led to his losing the kingdom.