The main trouble with a flat battery is that if it is not attended to quickly, it can lead to convenience failure, such that the doors will not open (even with the key).
The other main issue with leaving a flat battery is that lead-acid batteries deteriorate quickly if left flat, and hold very little charge when re-charged. They last for years if kept charged. I have an old car that has been off the road for many years. One new battery failed within a couple of years due to me allowing it to go flat and stay that way too long. I now charge the replacement weekly with a trickle charger on a timer, and it's holding up very well.
Bear in mind that batteries have gone up hugely in price due to a quadrupling of lead prices. It would cost in to buy a trickle charger (Gunson does a good one) and remove the battery for regular timed (or continuous) charging. You could get a solar charger for this rather than a mains one, and leave the battery in.
Other things to be aware of:
1) Brake disks will rust up if the car is outside.
2) Change the oil before laying up.
3) Check the tyre pressures. You don't want it sitting on a flat tyre for months.
It would probably cost in to keep the car. It will depreciate, but A2s are pretty good. The depreciation can be off-set against the cost-to-change, particularly if you sell to & buy from a retailer. The time involved in finding a replacement is not to be underestimated, particularly if you don't want to pay over the odds.
Mark