My company offer support, but this is for sites that we have implemented ourselves. They usually get special rates and pay once the work is done, this is due to a working relationship already being in place.
Depending on the cost you put on work it may be advantegious to take 40% upfront, this will tie in the client, and keep you happy that they're good for the money while the work is undertaken.
For small amounts of work, I'm just updating some site imagery at £50, I'd ask for payment on completion.