There's no set standard. It depends on a lot of variables, such as 1) what is their position in the car (ie: are they on the right side of book value, did they finance it, how much have they spent on reconditioning, etc) 2) are they a privately owned lot or a part of an auto group 3) what is their market like and 4) is this a valuable car to have on their lot.
How they are positioned on the car means a lot, but the biggest driver is going to be if they financed the car. If they utilized floor plan financing to purchase the car, say from auction, then they're going to be paying interest on it each month. In that case, a common threshold is 60 days. After 60 days, they'll run it through auction and see if they can get an acceptable number. If not, they'll pull it off the block, maybe lower the price on their website or offer a "spiff" to their sales staff on that unit and put it back through the auction again in a weeks time. Looking at another way they acquire cars, if they took it in on trade and closed the overall deal in a good position (close to or under ACV- Actual Cash Value), they can afford to keep the car on the lot for a while. On the flip side to that, if they took it in on trade and it wasn't a great deal for the dealership overall because of the final sales terms and/or reconditioning costs for the trade-in, then they might be more incentivized to get the car off their lot to recoup some of their costs.
Another factor is what
kind of dealership this is. Is it a privately owned dealership or a part of an auto group? This is important because in a privately owned dealership, the owner has greater flexibility to determine how long a car can sit on their lot. In an auto group, which is exclusively where I worked, the GM and Used Car Sales Manager only have so much latitude before being instructed to make an attempt to move off a unit through auction. They may have to start making moves at 30/60/90 days (just a general threshold number, although that's what my dealership used), with each milestone bringing different levels of action. For example, at my old dealership, 30 days meant a spiff for sales staff (an incentive bonus to whoever sells the car). At 60 days, they would up the spiff, but also run the car through auction. It didn't mean they had to sell it at auction, but they needed to at least run it through to see if they got a winning bid that they could accept. At 90 days, it was either sold at auction no matter what, or sold to another dealer within the group to see if a different market could get the car sold. I'll tell you, if a Sales Manager or GM have too many cars hit that 90 day mark, their time would've been very limited at my store as well as any store within our group.
You also have to look at your market. Do you live in a highly populated area where the dealers move a high number of cars each month? Or do you live in a smaller area where your local dealerships would have limited stock (in comparison to bigger metro dealerships) and in turn, sell fewer units each month? That will also play into how long a dealership will accept keeping a unit on their lot.
Lastly, is it a valuable car to have in their inventory? In other words, is that car bringing people into the store even if they're not buying it (could be a trim level, model, color, etc)? For example, we sat on a Plum Crazy Challenger with the 5.7 hemi and 6 speed auto for months simply because if we parked it out front, people would stop and look at it. In fact, we had people coming in from surrounding towns to look at it and test drive it because it was the only trim level (R/T) that came with that engine/trans combo outside of the very expensive SRT trim. By the time we finally sold it through auction, it had been the hook that got us a hand full of other deals that we might not otherwise have had. We could make a business justification sufficient to keep it on the lot even though we had financed the car and were paying interest each month, simply because it was helping us bring in other deals. A 5 year old Kia isn't going to have the same effect, so dealerships would likely pull the trigger on auctioning the car.
All that to say, there's no real way to determine how long a dealer will sit on a car. There's too many factors and the used car price mania, and the current drop in used car values is having impacts that only those currently in the business could understand because we've never seen anything like it.