Android - How frequently is it okay to let the battery discharge fully or as low as possible?

once or twice a month a full battery drain and then a 100% charge helps increase the battery life

That is incorrect, a full discharge is never beneficial to LiON battery capacity. The battery life of a LiON battery is dependant mostly on temperature, discharge rate, and age. In fact, low charge state actually is harmful to LiON battery capacity; although modern batteries have circuits that tells the system to shutdown before it became really harmful to the battery, it is best for LiON battery to be plugged in as often as is convenient.

also gives more accurate battery readings.

As for calibrating battery meter by full discharge-recharge, that is partially true. Modern smart battery comes with a microchip to keep track of the state of charge. The following is a quote from HP regarding Smart Battery System in their laptops:

Repeated short discharges and recharges cause increasing inaccuracy between the state-of-charge of the battery and the Power Meter readings. Periodically, the battery needs to be calibrated to "relearn" its usable capacity so it can synchronize its charge status with the Power Meter. ... The user simply has to periodically discharge the battery until the 5% capacity alarm is received. The need to perform this procedure will vary with individual use. In general, a Li-Ion battery should be calibrated a minimum of once every 3 months. A battery that is seldom discharged completely should be calibrated about once a month.

and the following is from Battery University:

How often does a battery need calibrating? The answer depends on the application. For practical purposes, a calibration should be done once every three months or after 40 partial cycles. If the portable device applies a periodic deep discharge on its own, no additional calibration will be needed.

The need for calibration comes from the mismatch between the battery's chemistry and the microchip that estimates the battery's state of charge. This mismatch develops over numerous partial discharge, although unlike the memory effect in NiCad battery, it does not affect the battery's actual chemical capacity and is reversible by letting the battery relearn its bottom and top charge state. Do not do calibration too often since deep discharge does permanently harm LiON's actual capacity.

For this question you might want to check with the Wikipedia article on LiIo batteries. Quoting:

• Avoid deep discharge (depletion) and instead charge more often between uses. The smaller the depth of discharge, the longer the battery will last.
• Avoid storing the battery in full discharged state. As the battery will self-discharge over time, its voltage will gradually lower, and when it is depleted below the low-voltage threshold (2.4 to 2.9 V/cell, depending on chemistry) it cannot be charged anymore because the protection circuit (a type of electronic fuse) disables it. [...]
• The rate of degradation of Lithium-ion batteries is strongly temperature-dependent; they degrade much faster if stored or used at higher temperatures and may even be stored in a refrigerator.

The first point already answers your question: You'd better avoid to "deep discharge" your battery. Best is to always keep it on 50% or up, but 20% should already "cry" for a charger. There's no memory effect or the like, so no need for that.

You might refer to the so-called "battery calibration" -- which today is called a myth by most, as explained by Google developer Dianne Hackborne.

If you think a "full charging cycle" (that is what you describe) might be useful from time to time (also see Lie Ryan's answer for this), make the interval between them as large as possible. IMHO multiple times a month is much too much -- once every 3 month should be enough. In that timeframe it might even accidentally happen you nearly "run out of juice" unwittingly, so you can use that "chance".