There are two aspects to look at here, curing the symptom or curing the cause. The symptom may be cured by changing the rest from a thin wire arm rest to a thick hooked wire arm rest such as the Spiagrelli magnetico or Cavalier elite rest or to a hooked plastic rest such as the Hoyt Pro rest. For each of these rests will give a greater stability to the arrow at full draw and will allow the novice to shoot without worrying about the arrow coming off the rest. However we will look at the reasons why this might be happening and this will always be to do with a tab, string interface. Many of the “old wives” explanations as to why this problem occurs such as “pinching the arrow” are wrong.
Firstly look at the contact between the tab leather and the nocking point area on the string. The groove in the tab should be as wide as the nocking point, any marks on the tab leather to indicate that it is contacting with either the arrow or the nocking point at full draw means that this gap should be widened. Next look at movement of the fingers on the string during draw, if there is any movement of the string from the starting position on the tab to the position at full draw then this will cause the arrow to fall off the rest.
Finally, and most commonly, flexing the wrist during draw will cause all of the above issues and is seen in many novice to intermediate archers. If the problem persists, get a coach or shooting partner to watch you drawing the bow an indicate if there is any side to side movement of the hand or wrist with respect to the forearm during draw. If there is take a lightweight stretchy band and practice the draw movement with increased weight until you are confident to make the draw without this unnecessary flexion.