Have you sorted this problem yet?

All alarms will flatten your battery eventually, ive got a Toad AI606 on my cabriolet, that stood for a good 5-6 weeks and was still able to start (just), your clifford alarm should be very effecient, read the documentation, i bet it boasts about how the whole system in armed mode consumes less current than the warning LED (most alarms are like this now), if your battery is a bit dodgy then it may well be going flat in a couple of days, the cold weather rapes batteries, even a car with a poor battery and no alarm at all will having difficulty starting THE NEXT MORNING. Get the battery tested its free, and if your buying a new one spend a bit of money, cheap batteries are cheap for a reason, like everything!! Automotive batteries were never designed to be flattened, but are usuaully ok being flattened occasionaly, but repetitive discharging will kill it, and usually if its on its last legs and it gets flattened that too will top it off.

Im assuming that link was for a solar charger, very good in my opinion, i used to work for Maplin once upon a time, they are excellent for just trickle charging the battery if the car is to be sat for a long time, but if you say you dont use it much then im guessing you have it garaged? If it is garaged, whats the harm in disconnecting the battery? Unless you feel you need to use the alarm. Give me a shout if you want any more help or get stuck