Having only being diagnosed 4 months ago I'm learning everyday!
No matter what I eat, brown rice, pasta, bread, cereal etc my blood sugar peaks 3 hours after eating. I'm on Humalog which is supposed to peak at 1.5hrs so readings are great at 2 hrs but a bit high at 3 hrs. I'm a bit wary injecting any later than immediately after eating
I'm assuming that you take some form of long acting insulin. It may be that you dose on this is too low and not holding you steady. The way to test this would be to have a carb free meal (A salad or skip a meal). Your levels should stay around 2m/mol of your last readings.
I get the idea however what's confusing is my bg drops 2-3ml over night unless I eat 15g carb snack. Even during the day I need to eat snacks of fruit or crisps between meals or my readings drop real low. I only take humalog with breakfast and dinner.
The doc dropped my lantus from 6 to 5 units thinking it was dropping my bg rather than maintaining it. I'm obviously still in the honeymoon period.