Any battery problems, it's worth checking the voltages (before replacing anything, TBH, but too late in this case).
I would do as follows:
Ensure the battery is reasonably fully charged. If in any doubt charge it at 2-3 amps for an hour or so.
Let the battery rest for a while after charging and connect a multimeter on volts across the terminals.
With no load the reading for a good battery should be around 12.5 - 12.8 volts.
Switch on the headlights and watch it for a few minutes. Voltage will drop to perhaps 12.2 but if it continues to fall to below 12 and the battery was charged at the start, battery FUBAR.
Now start the engine and look at the voltage at normal idle, fast idle, and fast idle with a good few electrical accessories on (headlights, blower fan, heated rear window, etc.)
I would expect to see 13.5-14.5 volts at idle, 14-14.5 at a fast idle and it should hold over 13.5 with plenty of accessories on, at a fast idle.
Any lower than this and the alternator is not charging the battery adequately, which may explain it not recovering form a flat battery after a drive. Higher than 14.5 and you have a regulator failure in the alternator and risk damaging the battery and other electrical items.
If the charge voltage is low, check all connections between the alternator and battery including chassis negative connections and straps between chassis and engine. Failure of the crimp connection at the positive battery terminal is a favourite (poor connections will get warm while the load is on them, which can help identification).
Kevin