Please note I am not a doctor. Always follow your doctors medical advise. They are qualified an they are responsible for accurately advising you and guiding you. The following is just my opinion as a patient.
First....in my opinion in people who suffer from 'low blood sugar' attacks, who don't meet the simple test method any doctors surgery or nurse can do.....
Check what your actual fasting blood glucose and/or post prandial results are first of all. Many doctors are cynical about non diabetics because they are used to seeing very low levels, conversely others with diabetes will tell you they feel wobbly and faint (and nervous) before their blood glucose is officially low! These are the people I speak with, people who have to monitor their glucose daily, they know what's up as they suffer the consequences of not monitoring their sugars with a monitor every day. So they tell me what PWME also say (interestingly), they can also feel really sick, eve without ''officially'' low levels, just 'low normal' ,or very near low. Maybe this is due to both conditions being associated to Autonomic Dysfunction as well, who knows. (Diabetes often have neuropathy, and some have POTS).
So that's the first hurdle. Find your actual level.
On the basis it's low normal..... I'm then thinking the following.
PWME or 'Chronic Lyme' report episodic low blood sugar attacks or feeling like it, that respond to immediate consumption of glucose. Some even say they have to eat all the time and don't just get re-active hypos (post food), and they are getting fasting hypo's. No cause is found, perhaps though, as they don't have all the tests - so we can't say 'no cause is ever found' for sure, as most patients have limited tests, or are too ill to have the more complex ones that need to be done in Hospital.
You could say that's inevitable as the brain uses huge amounts of energy and in ME CFS, mitochondria is slammed. Hence, the brain is maybe running a lower glucose level anyway (cerebral glucose) and coupled with autonomic dysfunction, we're probably super sensitive to brain glucose going lower than it should. This is all theoretical. More likely it's to do with crappy hormonal regulation in the brain, due to chronic low grade inflammation (my hunch), hence you 'mimic' other endocrine disorders, without having them as it's centrally mediated dysfunction (brain) not organ mediated (pancreas or adrenals).
Having a 'hypo' was one of my first symptoms with mild 'CFS' (no hint of ME), before coming down with severe housebound ME, so years before I got like I am now, I used to go everywhere with a candy bar and coca cola 'just in case', which once I knew that was involved, reversed the symptoms and was less terrifying when the symptoms hit.
I first got it exercising (when I had mild 'CFS'), and would have to eat copious amounts of food to 'reverse' the attacks that without made me throw up or start shaking violently, going freezing cold after swimming, playing tennis etc.
Now, here's where it gets interesting: Autoimmune POTS patients (tested myself already) often have ME. There's an antibody adrenal receptor than can affect insulin secretion, so maybe, people with this autoimmune problem have an 'immune based' random hypo event due to insulin levels fluctuating?
If you have ME or CFS or Chronic Lyme:
I'd do the following if the doctors are stumped after running a basic morning (fasting) blood glucose and it's hovering above the cut off limit for clinically proven hypoglycemia.
*Fasting insulin levels and post prandial (after a meal).
*Baseline cortisol and ACTH levels together (must be together). If they're low, you'll probably then get an ACTH stimulation test to rule out Addison's disease.
*Check all other pituitary hormones if possible and Thyroid is important.
More advanced tests...
*Glucose tolerance test in hospital (12hr fast beforehand) to rule out provoked reactive hypoglycemia (you drink glucose in the hospital and 'wait').
*Growth Hormone deficiency stimulation test (multiple ways of doing this). This is important as low blood sugar events can occur in Adult Growth Hormone deficiency. It's rare PWME PWCFS get this test, if at all If you look up the symptoms of Adult Growth Hormone deficiency, they may not be 'ME', but they are rather similar to CFS (including shortness of breath and prone to anxiety/panic attacks). There's no reason why patients can't have both conditions.
Failing that, I'd test all your nutritional markers in case your very deficient in chromium or something that helps regulate blood sugar, however, this may not be the problem in the end at all, and something far more simple.
As frustrating as it is, you have to stick with the doctors advice, even if it's slow and takes months. And if you're getting nowhere, think outside the box and suggest other ideas and see what they think.
Good luck.