i think that is the typical workflow (deleting after merge)
EDIT
So, rather than merge, at least for short lived branches, i think the idea is to rebase them on to the master. then you end up with a linear change history, and the entire branch becomes part of the main trunk. in this case you have all the changes there so you clearly don't need a copy.
Delete after merge is the usual way. This is why git branch -d yourbranchname checks to make sure that the branch is fully merged before it will delete.
There are a few reasons that I can think of to keep a branch around: you might want to hold onto it in case you have bugs coming back once it hits production, or you might want a historical record.
In either case, you have the option of tagging the head of the branch before you delete it. A tag is like a branch in that it is a pointer to a commit, except for a few minor differences: 1) porcelain usually doesn't display tags in exploratory commands like git show-branch or tab-auto complete in checkout, 2) checking one out puts you in a detached (non-ref) HEAD 3) you can leave a "tagging message", which causes the tag to be saved as an object in the object store like a commit.
This way you preserve history, and if you ever do need to bug fix, I recommend just creating a new branch off of master for the fix.
I delete after merge, but I always do a git merge --no-ff, to avoid fast forwarding so that the branch history is visible on the graph. I like to have the history of where the feature branch departed from the development branch and where it joined back:
This is taken from A successful Git branching model by Vincent Driessen, a very nice workflow to use with git which I apply for most of my projects.