When I went thro' this situation with my dog, she was up to date with wormers, the Vet stated if it's not worms irritating her, then it's the anal glands!!
Basically, itchy bum time!!
It came down to a good diet, regular wormers, and good grooming and hygiene.
Some pups, have a 'bum-itch' issue when getting used to various things like weaning, getting into a regular worming regime, and if not caught/stopped early can form a habit, even if they have no symptoms.
Older dogs become less able to clean themselves, or 'toilet' properly due to arthritis/pain/fatigue...they're just old dogs becoming slower in their years, and their metabolism changes and do not require the same nutrients from food as they did a few years ago.
There's quite a few factors to consider changing in your dogs life as they age.
Apologies for the sermon, but I did begin to despair with my old dog, and learnt quite a lot during her treatment.
Good luck, it'll take a bit of getting used to, but it really was worth it.
Regards
B-Liner