2005 Pontiac Sunfire battery drainage

I was told that a remote starter can drain your battery, is that true? Had the original battery for 6 yrs with the use of a remote starter and never had any trouble. Since I change my battery, it doesn't last more than 10 months. Have had 4 new batteries in the last 3 yrs and was told it was because of the remote starter. Just want to verify if that could actually be the problem.