Could be a couple of things.
Sometimes they'll go next to the litterbox (or in other places) if the litterbox itself isn't as clean as they'd like it. I know you said you were cleaning it, but you might want to try throwing out all of the current litter, and giving the box a good scrubbing both inside and out (including the bottom).
With the increased urination of the diabetes, there may have been times that she just didn't quite make it to the litterbox. And sometimes when they've started going in an inappropriate place, they'll continue doing so. I'd give the the area the box a good scrubbing as well. You might try using some white vinegar; that'll get rid of the smell of cat urine, even if you can't smell it, she possibly can, and they can use scents of previous uses indicate that this is a 'safe peeing place'.
Finally, it may be either painful or difficult for her to get into the box, and the timing of her problems may or may not be related to the diabetes. For example, a lot of cats with arthritis find it painful to climb over the sides of the box, and some cats who have had uncontrolled diabetes (or who have diabetes that is under-controlled) develop a condition called diabetic neuropathy, which makes the legs weaker. The solution here would be to address the underlying health issues and make adaptive changes as needed.
For example, a cat with arthritis might be put on arthritis medication (Cosequin, Dasuquin, Adequan, painkillers, etc), and might benefit from either a ramp into/out of the litterbox, or from a litterbox with a lowered lip such as those pictured
here (for various reasons, I'm particularly fond of the 'mini' one. It's for miniature dogs, and it's bigger than a normal cat litterbox.)
In a cat with neuropathy, you can use an adaptive litterbox, or you can just live with the situation until the neuropathy resolves. Neuropathy in cats will heal itself as the cat becomes regulated on insulin. Depending on the degree of neuropathy, that may take some time. The typical symptom of diabetic neuropathy in cats is that, instead of standing/walking on their 'toes' with their rear legs, they walk lower on their feet, sometimes with their entire 'foot' touching the floor (this is called a plantigrade stance).
As I said, neuropathy in cats will resolve itself once the diabetes is under control. You'll find a bunch of folks on the boards here have also used a supplement called methylcobalamin; that's the methyl form of vitamin B-12 (the regular form of B-12, cyanacobalamin, won't work for this). Methylcobalamin in and of itself will not stop diabetic neuropathy, but it may help slow the progression of the problem (if the cat continues to be unregulated / under-regulated), and it may help speed healing once the diabetes is under control.
If you suspect that urination may have occured in other inappropriate place, you may want to get a black light, available in the fluorescent lightbulb section of some hardware/home supply stores, or a flashlight-type thing called StinkFinder, available in many pet stores. Wait until dark, turn all the lights out, and hold the light a foot or two off any suspect surfaces. Urine (and other stuff) will fluoresce in the light, making it easy to spot and clean up stains. You can use white vinegar on most hard surfaces or, if the item is washable, put it in the laundry and add a cup of white vinegar with the detergent (two cups if it's a thick item like a pillow). You can also use a 50-50 mix of white vinegar and water on carpets, or you can use an enzymatic cleaner.
HTH --
Jean and her Gwyn
![JJ & Gwyn [GA]](/FDMB/data/avatars/m/0/167.jpg?1419296044){kind=avatar}
