Some of the older Morgans (mine included) have a battery isolation switch fitted which will prevent this. If security (insurance) is not an issue you might consider having one of these fitted by your agent or DIY. This is in itself a very good security device and I always use it when playing away from home.
http://www.holden.co.uk/displayproduct.a...mp;pCode=SSB112The ECU soon relearns once it's temporary store has sorted itself out on power restoration and a few miles 25 or so.
Hamwich's answer sounds like a really good alternative too given that you have no power outlet or sun.
p.s. In my earlier reply I assumed you had a Gel battery fitted in the engine bay I hadn't realised they had reverted to somewhere sensible.
