Unlike airlines that charge customers higher fares the closer to the departure date you make your reservation, some car rental firms actually lower the price as the rental date draws nearer. They don’t advertise that fact, they just do it quietly.
Example: MrConsumer helped a friend book a 12-day rental starting on August 22 from Logan airport in Boston. At the end of July — approximately three weeks in advance — the total rate including taxes was in the high $400s for Alamo — and that was using a coupon and a group discount.

Exactly two weeks before the start date of the rental, just for the fun of it, MrConsumer checked prices again at Alamo on a new reservation, using a better coupon — $40 off a 10-day rental. Between the coupon and a new price reduction, the exact same rental dropped to $420.
*MOUSE PRINT:

Not bad, a savings of about $60.
Checking prices again exactly one week before the rental was scheduled to begin revealed another price drop of close to $100. It was now down to $337.
*MOUSE PRINT:

Wow, that’s a total savings of almost $150 compared to the price that would have been charged on the earliest reservation.Â
And, checking the rates one day later, the price dropped to $317.
Now, on August 17, just five days before the rental, the price dropped again:
*MOUSE PRINT:

We are now under $300 for the rental, an almost $200 savings compared to the price quoted at the end of July.
It can’t get any lower, can it?
*MOUSE PRINT:

Wow.. as of Wednesday, August 18 — just four days before the rental — the price dropped over $30 to $267. Will the discounts ever end?
Two days before the car rental was scheduled to begin, the price dropped one last time, albeit by only $7.
*MOUSE PRINT:

Just to finish the price history of the rental, the day before the actual rental, the price jumped up to $414.91. And on the day of the rental itself, the price was $434.68. Amazingly, the highest price Alamo offered was the first one — for the reservation made over three weeks before the actual rental date. The total savings for MrConsumer’s friend amounted to over $220 by making weekly, and then daily checks of prices as the rental date drew near.
Surprisingly, in this case, it was substantially cheaper renting at the airport than from an in-town location. (The opposite is usually true.) Compounding the problem of high rates is that string of junk fees and taxes that boosts the price substantially, no matter how low the published rate is per day.
Because no one knows if prices are going to go up or down in any particular case, or with any particular car rental firm,  it is still wise to book early (using all the discounts and coupons you can find), but check again repeatedly  as the rental date approaches. If you find a lower price, book the new reservation, then cancel the old one.