If you have a creature bound from a previous casting of Planar Binding, can you cast it again at a later point to renew the duration? I don't see any reason why not, but I may be missing something.
Yes, you can.
The rules for Combining Magical Effects specify that (emphasis mine):
The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect--such as the highest bonus--from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.
Hence, if one casts Planar Binding once and after a while they recast it on the same target, just the last casting takes effect.
For example, suppose that a Wizard successfully casts such spell on a fiend at Monday noon: until Tuesday noon they can control the fiend. If the Wizard successfully (i.e. the target fails their saving throw) casts again Planar Binding on the same fiend at Tuesday dawn before the ending of the previous spell, the duration of these spells overlap, and only the more recent one takes place: hence the wizard will control the fiend until Wednesday dawn.
A caster can attempt to gain control of a creature one day after another, simply casting Planar Binding one hour before the ending of the previous casting: remember that this does not automatically extend the duration, but the target has to fail their saving throw each time.