I personally wouldn't be able to chase them but it wouldn't be a problem for me, as I always go shopping with my sister. She's a police officer and would chase them down, catch them and have read them their rights (and possibly their future - jk - >lol<) all within a few seconds.
Yvette, I am not trying to dismiss your discussion but having a sister as a police officer makes me feel that I have to add the following to the discussion:
The police strongly recommend that you do not chase a bag snatcher, whatever your level of disability and level of fitness, even if you're a Paralympian. They may well be desperate, armed and willing to seriously harm or even kill you. If you caught up with them, they're not just going to hand the bag over. Most of the criminals my sister deals with aren't "it's a fair cop, guv" types (not saying you think that, Yvette, but others might). They will think nothing of seriously hurting someone who chases them and wouldn't hold back just because the person is disabled or elderly.
While it wasn't a bag snatch, look at what happened to Graham Buck, who was murdered defending his elderly neighbour during a robbery. It shows what lengths a robber will go to. I worked with young offenders and I'd have to say that many of them wouldn't think twice about stabbing someone who tried to chase them and get their bag back. In their world, you're trying to take it off them. They see it as "if they're disabled they deserve to get stuff taken off them". Their world is very much survival of the fittest.
The police also advise that you do not keep items (eg photos) which are irreplacable in your bag or purse/wallet. If you want to carry a photo around with you, get copies made and keep the original somewhere safe. That way, should the worst happen or you lose your bag/purse/wallet, you won't have the added heartbreak of losing something that means a lot to you.