First thing, are you eating the proper diet? Most of us on here, when we get our diets right, have no symptoms or rarely get anything that causes any major problems. Here's some things I would say.
1. You need to first explain how hypoglycemia works because people usually don't understand it. Explain that the brain can only run on one form of energy to function at full capacity and that's glucose. When normal people eat and their blood sugar goes high, the pancreas shoots out insulin to keep the glucose level in the blood normal. In hypoglycemics, however, the pancreas secretes too much insulin and does it continually throughout the day. The problem then is that the blood glucose level does two things. One, it drops too low and two, it drops too fast for the brain to have time to adjust to the level. Since it realizes it is running out of fuel, it begins to shut down areas of the body (typically sections of the brain itself) that are less necessary to basic functions. The heart and lungs, for example, need to always be running, so those are kept active. Other things, like the neocortex (responsible for mood, concentration, thinking, following social rules, etc.) are not necessary to keep alive so it shuts them down or diverts glucose from these areas. When this happens, the hypoglycemia can become extremely depressed, anxious, irritable, sleepy, get blurred vision, become confused (forgetting where they are perhaps) and a host of other symptoms in a matter of minutes. There is nothing to do and this can't be "shaken off" like i've heard some people say to me. The brain has no energy. If you were driving a car and ran out of gas you couldn't exactly tell it to "shake it off," you'd have to put more gas in it and that's all we can do. Unfortunately, unlike a car which can then run on gas as soon as you put it in there, if a hypoglycemia gets a bad drop in blood sugar it can take a few hours (at most) to restabalize. Tell them all of this.
2. All hypoglycemics eventually learn their own body triggers that are signalling something bad is coming. Sometimes they'll know it because they tend to get sleepy before it happens, or perhaps angry at the strangest things suddenly, or perhaps get a weird feeling in the stomach, anything. These signals mean the sugar is beginning to drop to below normal. Because of this, we also know when we need to eat, so it's easy to catch the drop before it gets too bad. Sometimes we may be a little below functioning capacity when this happens, but who isn't throughout the day? If we don't eat, however, it will get worse so that needs to be stated.
3. Because hypoglycemia is a disease (if you haven't been tested and have the paperwork to prove it I suggest you figure out a way to get something through your doctor), your employer needs to be able to accmodate you when you need it. This doesn't mean special privledges, but there is always something they can do to accomodate you when you may be having a terrible sugar day. Perhaps paper filing, fixing a schedule, anything other than what you are considering "liable" for. I used to work mental health when I first got hypoglycemia, and even when I was in really bad states of sugar shock I still managed to do the most taxing work, so it can be done. They can't just throw you aside because of a disease, that's not legal.
4. If you haven't gotten yourself on track with the right diet yet I suggest you do, and furthermore I suggest that you see if your employer has medical leave. Take full advantage of it and burn as much of it up as you can to take as much time off as possible while you get your diet on track. When you go back to work, ask your employer to let you ease back into the workload gradually, perhaps going from 40 hours a week to 20 and then slowly building back up so you're ready for it.
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