unkeljoe: "braking all the way down a steep grade can cause your brakes to overheat and become temporarily inoperable. "
That condition is known as brake fade/fading and occurs mostly with drum brakes and can occur on bicycles, motorbikes and automobiles.
Braking heats the brake drums, which then expand. The drum may expand in diameter to the extent that the brake pads no longer contact the drum sufficiently enough to slow the vehicle. Your brakes "fade" away.
Many vehicles have disc brakes in front and drums on the rear, an arrangement usually sufficient even in hilly country. Of course when pulling a boat or trailer having all disk brakes would be a safer bet.
Brake drum fade is by far the most common manifestation, but there are other types of "fade", e.g., brake fluid can get heated up enought to boil and reduce braking system pressure, brake pads can "slip" more at extremely high temperatures:
http://bicycles.stackexchange.com/questions/30449/do-mechani...
Last ditch efforts: shift into a lower gear, use any emergency brake (which is mechanical and bypasses the braking fluid system and so won't fade due to boiling fluid), and finally, use the inside of a hill/mountain as a giant brake pad by sliding your car's body into it as gently(!) as possible.
Finally I feel compelled to warn anyone who ever pulls a trailer, boat or RV about a potentially fatal phenomenon they may encounter on even gently sloped roads: undamped driven harmonic oscillation between towed and towing vehicle. My first experience:
VW Beetle towing a U-Haul trailer on a Pennsylvania turnpike mountainside. Traffic moderate in both directions.
On a long downhill segment the trailer hitch began to move to-and-fro left and right, gently at first but, as I attempted to correct with steering, rapidly growing in amplitude. My steering reaction time and corrections were unfortunately timed precisely so as to _increase_ the amplitude of the oscillation. In a flash the rear end of the Beetle was hopping right and left! Insight - I need to dampen the oscillation. I gripped the steering wheel, braced both forearms against my legs and reduced all steering corrections to a minimum (I just kept the car on the road and in the proper lane). The car's front end skidded left and right as I kept the wheels as straight forward as possible. Then I slowly applied the brakes. This brought the oscillations under control and the speed down. I continued the trip at a much slower speed despite the honking of frustrated drivers behind me.
That first experience, enhanced by both impending ignominious death on a mountainside and the sudden realization of the utility of my mathematical physics class* [1], was exhilarating.
In the years since I have myself seen this occur several more times, which makes me think it must be a not-uncommon event that requires some warning.
It once again occurred on IH 10 between Houston and New Orleans, one of the flattest pieces of land in the USA. A heavy-duty six-wheeler pickup was hauling a trailer full of goods on an extremely gentle slope at near 70-mph when his trailer hitch began to oscillate left and right. I had been following and observing his truck and noticed that the system seemed to be periodically oscillating, so I stayed well back and did not attempt to pass even on a four-lane highway. Finally things took a turn for the worse and, within 6 seconds of back-and-forth oscillation and attempts at correction, both truck and trailer were driven off the road into the grassy median. Luckily the median was wide flat grass and no harm occurred to driver, truck or trailer. I stopped and crossed the road as the driver took off his cowboy hat, waved it at his truck and trailer as if dismissing an unruly horse, bent his back, and put his hands on his knees in amazement.
I spoke to him awhile, reassured him and gave as best an explanation to him of what I saw and what he might do to prevent further mishaps. He was quite out of sorts and I'm not certain he was fully able to absorb the lesson. He was definitely astonished to find himself on the median with his truck and trailer turned around 270 degrees from the direction he intended.
Had this happened on a strip of highway without such a wide median the truck would have driven at ~60 mph into ongoing traffic at 70 mph. Had this happened on a hillside, I would estimate a 50% chance of both vehicle and trailer plummeting downhill. For these and other reasons, I think this phenomenon must kill more than a few people each year.
More discussion of fish-tailing trailers:
https://www.google.com/search?hl=en&source=hp&biw=&bih=&q=tr...
Physics can save your life:
[1] http://hyperphysics.phy-astr.gsu.edu/hbase/oscdr2.html - Under topic "Driven Oscillator Example" the red curve describes the ever-increasing amplitude experienced.