question about charging battery

[Andy H]

While my car is in the garage for winter, It usually goes about 2 weeks before I take it for a drive. The battery is fairly new duralast gold. After a week or two the battery is almost so dead it won't turn the engine over. I tested the voltage output of the battery and it was 11.5 while it was drained. I also checked with an ammeter for a parasitic drain and it was only drawing .05ma. I have a small trickle charger. It's a schumaker 1.5amp automatic charger/maintainer for 6 and 12 volt lead-acid batteries. It is a model SE-1562A. Is it ok to hook this up and leave it connected for a few weeks? If so is it ok the leave the battery in the car and hooked up? Is it normal for my battery to drain in a couple weeks?

Thanks!