No mate, a battery should hold a charge longer than that.
If you have any extra power sockets fitted, are they permanently on or powered off the ignition?
Because if you have a USB socket permanently powered it will discharge the battery.
Charge and then remove the battery and keep it in the house for a couple of weeks, as the cold also affects batteries, then reconnect it and see if it will fire up, if it does chances are somethings draining it.