Hi Alfie,
This will make you feel better,
Alfa 156, low battery situation making the alarm disfunction is not
unique to your Alfa, most modern cars react in a similar way.
The disconnecting of the battery is usually the easiest solution, and
luckily it only means that the radio setting and the clock time is
lost, but easy to reset. On some cars if one disconnects the battery
then all hell breaks loose when one reconnects it, like the air bag
lights refuse to go out and other little irritating things which
require a trip to the dealers to reset the computer, (happend to me on
a Honda some time ago) Its Ok I drive a 156 these days.
Now the battery on these cars does seem to drain down quickly if the
car is left standing for a while with the alarm (energised) I mean if
you leave the car with the alarm set, as when you lock it via your key
fob, and the flashing "led" is active.

My car is only used at weekends and I have to keep an eye on the
battery situation, (there should be a green indicator on the top of
your battery ? )
this should show green when the battery is in a good state of charge,
as the battery drains down the green turns to black, indicating that
it needs a good long run, or to be recharged via a seperate battery
charger.
If you decide to do this, then disconnect the "neg" first then the
"positive" second, when you reconnect it is "pos" first then "neg"
second.
The Battery seems to remain "green" for about 3 weeks if not used but
with the alarm on, so I guess that after about 5 weeks it would be
flat enough to set the alarm into active mode, as the alarm will
detect a voltage drop, which is what it is designed to do, because if
someone  opened the car door, then the interior light would come on
and create a voltage drop, same as if the bonnet or boot were to be
opened, thats one of the basic sensors.
I often leave my car at an airport and I notice that in the paid long
term secure parking places the operators always leave the keys in the
cars, and they have to be left unlocked, ( they are safe and in a
compound), I used to think that I may come back and have a flat
battery, but not so, because the alarm is not active, ( can you
imagine all those alarms going off everytime a big jet went over the
car parks at gatwick, also it is incase they need to clear the area in
an emergency).
Head Lamp bulbs changing in a 156, childs play, so long as you have
fingers, it takes like two minutes, turn the cap, and remove it (under
the bonnet) and there is the plug on connector, gently prise it and
pull off, then there is a spring clip which you squeeze the tags
inwards and release the ends from the two
lugs on the lamp body, bulb pops out.
The secret is when replacing the bulbs, (two in each head light, plus
a side lamp bulb) the glass must not be touched, use a tissue, and
refit but make sure the bulb is in the correct way round, note the
tags positions when you extract the original, you will notice as soon
as you turn your lights on, the beam will be have a strange spread
pattern. I would suggest that if you are changing head light bulbs
that a good idea is to buy the up grade "Philips vision plus type"
a much better "whiter light" better night vision.
Back to the car battery if you can or have a secure place to park over
night why not just lock it with the key  and not activate the alarm,
because for some reason the alarm on these cars does seem to drain the
battery quickly,  I understand that the alarm system is made by "Meta"
and are highly regarded and used by other manufacturers like those
German taxis/repmobile things from the Black Forest area.
Hope you sort it out, at worst a new battery, they only last about
between 3 and 5 years. One final point, when the engine is running
have you checked if the battery is charging, a voltage meter across
the terminals should indicate about 14.5 volts being put into the
battery from the alternator, and this decreases as the battery picks
up its charge, down to about 13.5 volts.
At least you will know if its a duff battery or if the car is failing
to supply the required juice to keep the battery up.
Regards Martyn.