I read a lot that opened wine bottle can last about 3 to 7 days when it is stored well in the refrigerator, but i want to know how long it will last in the cup. Thank you
Ultimately, it last until you decide you no longer like the taste. What's happening is that the wine is oxidizing, and the flavor and aroma compounds are being destroyed once they're exposed to a significant amount of air. While temperature does make a different, the larger factor here is the amount of surface area to volume, which is quite high in the glass compared to in the bottle. While a bottle in the fridge will keep it's flavor components intact a bit longer than if it were on the counter (and longer yet if you put it in the freezer) a bottle on the counter will still retain its character longer than a glass in the fridge, or certainly on the table.
Another factor to consider is how well aged and tannic the wine is. All red wine is not made alike, and a young tannic wine will hold up better for longer (and indeed even improve for awhile before it starts to degrade) compared to a wine that's well aged and already at or past its peak.
In any case, you're probably looking at a matter of hours. While I've never paid close attention, I would guess that depending on the wine, an average of somewhere between 6 and 12 hours is going to be the limit before you start to see noticeable degradation. It could be more or could be less, but not by an order of magnitude.