Sorry to hear you are having so many hypos. I was informed by my DN that in the event of a hypo, take your jelly babies, or coke to bring you BG up, but to follow this a small carb meal, toast or sandwich, in order to prevent the occurrence of another hypo. This has been my way of treating a hypo.
Are you finger pricking to confirm the L2 reading? I have found the L2 will read lower than actual BG reading when the L2 readings get into hypo territory. As already mentioned, compression lows are relatively common with the L2 as well. What do you have the "low" alarm set at? Mine is set at 5.0. I find that when the alarm goes off, I have time to finger prick and if necessary start taking action to avoid a hypo
Is it possible that you are over dosing your insulin with your evening meal? I have heard of diabetics who rigidly take a set amount of insulin per meal, every meal. I can't see the logic in that personally. Why would you take the same amount insulin for a chicken salad as you would for meat pie and chips? The carbs in each are vastly different. I take my BG reading before each meal, and calculate the amount of carbs in my meal (as best I can), I then adjust my insulin dose to suit. I also set a timer for 1 hour and 2 hours after each meal to check if my calculations were correct, and the insulin did its job effectively.