I would say starting the generator every two weeks is excessive unless you want to get away and read a book for a while. Especially in the cold climates, generators sit for the entire winter without being started. Getting them started at well below zero (uless there's a definate need to use the generator) is harder on them than not using them.
Your starting batteries shouldn't have gone dead in one month. If you had the batteries disconnected using the disconnect switch and this still happened, then either the batteries are in poor condition or something is drawing too much load around the batteries somehow. The battery disconnect doesn't shut off everything 100%. If the battery disconnect was used and you don't know what's drawing the power anyway, then you need to disconnect the batteries when you store it for a month or longer.
Mine sat in storage from about Oct 10th of last year until May 17th of this year and the MH cranked up just fine. That was seven months. The batteries at 2 - 3 years old and left in the MH all winter, but they were fully charged and the cables are disconnected.
Bill