A few things come to mind...
Bad battery (even new ones can go bad with intermittent internal connections)
Corroded battery terminals or battery connections...
Clean with this to a bright finish...
Battery Terminal Cleaner
and apply some motor oil to the freshly cleaned terminals..
A parasitic current draw (usually from add ons or accessories) from (GPS/non-OEM radios/radar detectors/cell phone chargers/etc... Also there could be a problem with a microcomputer/microprocessor like the BCM (body control module)...KIA Spectras had this problem where the Auto-Headlights would come on in the middle of the night and the owner would come out to a dead car...An upgrade to the firmware in the BCM cured this problem...
You said you replaced the alternator...If the "re-manufactured" alternator came from advance or AutoZone they have been selling "re-manufactured" alternators that were really only repaired and cleaned up...These repairs were done in Mexico and if the alternator you got was intermittent or the problem did not show up during their "testing" they just cleaned/reboxed/and sent them to these stores...You loose!
They have a "Lifetime Warranty" because they are sooo profitable and have a high defective return rate....
A truly re-manufactured alternator will have these parts replaced... Bridge rectifier pack...Voltage regulator module...both bearings...new brushes...new insulators...
Then the armature and the commutator would be "turned" on a lathe and the alternator would be checked for a period of time in a "real life" scenario...
This repairing/rebuilding problem happens also with starter motors repairs....
I would not buy one of these "gems" and would buy either a NEW alternator on ebay or have mine rebuilt by a local starter/alternator rebuilder.
I base my diagnosis on the information of "clipping on another battery source" bypasses the current battery and battery connections and also provides a source to start the car that could recharge a dead/flat battery...
I would also suggest you do a specific gravity test on the battery BEFORE trying to start the car...This will tell you "if" the battery is charged (or not)...
Battery Specific Gravity Test: Battery Hydrometer Test
You want to do this BEFORE starting the car so you will know the results before the alternator has a chance to recharge it...
Bring your results back to the forum so we can provide more help to you or others...
Dave