Hi, Julia,
Many cats as they get older do lose teeth - a heavy deposit of tartar builds up, and looosens the tooth, which eventually falls out. When the teeth get into that state, the cat is usually better off without them.
You do not say if he is on insulin injections for his diabetes, nor how old he is. I found it to be difficult to stablise diabetes in cats, even with insulin injections - they tend to be very 'picky' about their food at the best of times.
Have you taken him to your veterinarian lately for a check-up - blood glucose etc? Regular veterinary checks are essential.
Hope all goes well.
Walter