Sounds like you have a charging problem.

If you have replaced the alternator and still drained your new battery, then the alternator (replacement) could be faulty too.

Have you checked the ALT fuse? could it be blown?

any wires grounding?

possibly a loose alternator harness plug too... - clean it up as they are caused to have dirt and shit in them and if the terminal pins are shit then it could play up.

Have you got the correct Alternator replacement? all alternators are different in their Voltage Regulator charging AMPS/Current output. so if you have the incorrect one or its faulty, then you have a drained or burnt out battery.

A part of the charging system that controls how much electricity the alternator puts out. The voltage regulator on modern cars is an electronic black box, which means you can't adjust it or repair it if anything goes wrong with it. (your in the black hole)

On most newer vehicles the voltage regulator is located inside the alternator and cannot be replaced separately. On some cars, the powertrain control module (PCM) regulates the alternator. A defective regulator can cause the alternator to produce too much voltage (which can damage the battery, lights and electronic components) or it can prevent it from making enough voltage to keep the battery fully charged. The toughest challenge when diagnosing a charging problem is to figure out whether it's the voltage regulator or alternator that's at fault. Using a procedure called "full fielding the alternator" that causes the alternator to put out maximum current will reveal which component is at fault.

its weird that it only happens downhill - which telling us that the problem occurs when elevated. hmm ..

check the Volatage Regulator - first identify where it is. :P