chocobo stable getting dirty on its own

[Nicobo]

...is the stable supposed to get dirty on its own?...

Yes, it is time based. The condition drops one level every 72hours.
So previously when magic brooms were very expansive,
I cleaned the stable just right before next dropping to save magic brooms. ^^;

remark:
After you clean the stable, the condition will be dropped again after 72 hours,
so previously for max. saving, i cleaned it when it was fair condition and just before dropping to poor condition, so after cleaning it became good condition and could last for 3days.

ofcoz nowadays just clean it when it drops.