Once you open a bottle of distilled water the opened bottle of distilled water is good for around 7 to 10 days.
Keep the opened bottle of distilled water sealed with the lid when not using it and keep it out of heat and direct sunlight and it should be good for 10 days.
However after a period of a few days or so it begins to lose it's distilled qualities.
The distilled water itself will remain okay but it will no longer be distilled or at least considered distilled after 10 days or so.
If you never open the bottle of distilled water it can last basically forever and remain distilled basically forever.
Water itself really never goes bad and even when dumped out on the ground it gets evaporated or soaked into the ground and goes back into the water system.
You could be drinking water that rained onto the ground 100s of years ago.