I've been storing cars for 25 years. One month can drain your battery...keep it disconnected until you get back. I don't think one month will affect the fuel significantly. I've driven on 6-month old fuel! Though I agree with G-Benz. He's saying that rather than keeping the tank full, you may want to keep it near empty. That way you can fill up with fresh fuel when you come back.

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95 E320 Cabriolet, 169K