It might be that she is getting too much insulin, but I'd think we would see more movement. It is true that too much and too little insulin can look the same, but if she's been on 4 units since November and it's too much, at some point it seems like she might have crashed and dropped low?
If you want to try a reduction, I'd halve the dose. You could do an experiment and reduce back to 2 units for a cycle or two and see if the levels drastically improve. If not, then move right back up. And test for ketones if you lower the dose.
My gut says she needs more, but I have been wrong before and will be wrong again....it may be worth a try but don't stay there too long. We don't want her in blacks and reds, if that is what a lower dose gives you; the pinks and yellows are much better for her body.