What time are you picking up the car and what time are you returning it? Car rentals are generally based on 24-hour days. So if you pick up at, say, 11 AM and return at 9 AM seven days later, that's seven days. If you return the car at 11:30 instead of 9 AM, you're still within the grace period. If you return the car after noon that day, you start getting charged the additional per-hour fee until you reach the extra-day rate.
So say you WERE arriving at 4 PM Saturday, and now you're arriving at 3:45 instead. No problem. Your original departure was 2 Pm, so you were returning the car at noon; now you're bringing it back at 12:30 instead. Still no problem - you'll have the car for few than seven consecutive 24-hour periods.