I said "a good charger". To give you an idea of exactly how well a good charger works, REGIS has been using the same 5ah SLA (electronics) since November 2000. For most of that time, the battery is in use around 12-14 hours a day, 7 days a week, and is on the charger nightly. The battery has been frequently deep-discharged on more occasions than I care to count. Only recently is this battery showing possible signs of fatigue, and this is no special battery (Panasonic LCR1-125P1) . The same can be said of the 7ah sla that powers the motor, although it is charged much less frequently (and often deeply discharged).
So if I did nothing with the battery other than left it on a shelf and charged it monthly would it last longer? Possibly -- I certainly wouldn't take your bet. Even if you didn't win, I would have tied up a $60.00 charger for a year. (Not to mention that, honestly, I don't know you well enough to actually wager anything.)
Basically, if the battery is allowed to discharge, you'll end up with some amount of sulfation on the negative plate (not good). But charging the battery always carries some risk of erosion of the positive plate (also not good). A good, temperature-compensated float charge algorithm _should_ strike a reasonable compromise between the two, however, making the real difference academic. In fact, some float charge algorithms monitor the battery voltage and only apply a charge when the voltage drops below a preset value, essentially mimicking your "charge it once a month" approach -- the real difference between the two being that the user isn't required to remember to charge the battery once a month.