Technically I think the default from the rules is that it lasts the the earlier of the end of the encounter or five minutes.
However, I am not sure the default is applicable for a power like the one that you mentioned, which adds to diplomacy checks.
Either way, some sort of actual rest (as in break from the negotiations) is in order before you can recharge a power.
I guess the first question then is how many checks are you requiring for the diplomacy? If the diplomacy lasts several days, but you only require one check, then I would allow the power to influence the check one time. If you require a check each day, and the character rests for the night between each day, I would allow the power in influence each daily check.
I guess the real tricky part comes in diplomacy that lasts, say, 15 minutes, requiring three checks spread out over that time. The character does not have a break, unless they can work into the diplomacy that they get the chance to walk away for a bathroom break in the middle of the diplomacy. So in that case, unless they can get a break (to regroup their thoughts or remember an important fact that will help with the diplomacy, for example, as an explanation for how the power works), I'd only give them the benefit of the power for one of those three checks in the 15 minute period.
But really, we're talking about iffy ground here. The powers were probably not written with a lot of this sort of thing in mind. And that being the case, your guide is page 42 of the
DMG, and gauging whether this is a clever use of a power, whether it adds to the fun of the game, whether it is overpowering or will lead to abuse, and that sort of thing. Everything else being equal, I would side with letting the player use the power as often as they like, as long as it doesn't break things too much.