I think all radios with a memory have a slight draw--not sure how much,but even a factory radio will drain a battery eventually..I'd say a month is pretty good,considering if the vehicle also has a clock thats always "on",to help pull the juice out of the battery..
A battery can also discharge itself simply from being dirty...I never believed that till my shop teacher took a digital multi-tester and hooked the positive lead to the + terminal,and then touched the negative to the battery case--the film of crud and moisture was a good enough conductor to show a discharge..left in that condition long enough it can kill the battery after a couple weeks even with the cables not connected..
I had an elusive drain killing the battery on one of my trucks,I decided one day to put a test lamp between the positive battery post and the positive cable,and it lit up,indicating a draw --pulled every fuse out one by one,the light stayed on,so it wasn't a short or the clock,radio,or cigar lighter sapping it down...
I tried taking the big red wire off the altenator,hoping it was a bad diode causing a drain,nope,the test lamp still stayed lit up!...it wasn't till I tried unplugging the HEI power wire,that the light went off...it wasn't brightly lit,just a dim glow...never did figure out how power was getting to the coil with the ignition off either...I tested a few friends trucks,their showed the same dim glow,so I assumed its "normal"?...

..a new battery solved my "drain" problem...as long as I drove it every couple of weeks,it always started after replacing it..