Depends on your state and the insurance company. I work in auto claims in California, here we'd owe you for a comparable rental vehicle for a reasonable amount of repair time. So, if you have a Suburban, we can't give you a Nissan Versa rental car and say deal with it, we'd have to pay for a large SUV. If the estimate says it'll take 4 days, and it ends up taking 5 or 6, it can be considered "reasonable" and we'll cover it. But if the shops got your car for 2 weeks and doesn't have any reason for having it for that long (haven't found any additional repairs that need to be done or had any reasonable delays), you might get cut off. Depends on the insurance company and the repair, every case is different.
With that being said, what happens in 99% of my claims is that the initial estimate is written up, the car is taken to the shop, and the shop finds additional damages that were not on the initial estimate. The shop calls us, we add the additional repairs (and repair time), and cover additional rental days accordingly. I very rarely refuse to cover repair days for rental. The reason for this is that the intial estimate is written before the car is torn down, so not all damage is visible at the time of the initial inspection.
If the insurance company does cut off the rental before your car's finished for whatever reason, you still have a few options.
1. You can, of course, take the rental back on the last day the insurance will cover.
2. You can see if the shop will cover those rental days for you that insurance is not going to cover. This is actually fairly common, as you are the shops customer, not the insurance companys, so the shops tend to try to help out as much as possible.
3. If 1 and 2 are out of the question, you can pay for the extra rental days out of pocket and ask for reimbursement from the person who hit you. If they decline, you can take them to small claims court.
Let me know if you've got any other questions, especially if you're in California. If you're in another state, the above might not even be true, haha. But I'd imagine it's relatively similar is most areas.