No browsers support resuming uploads.
From my Googling, Flash doesn't seem to, either.
Though I don't know enough about Java to say it's impossible, there don't seem to be any pre-rolled upload solutions that support this method.
In short, you would have to code your own out-of-browser/plugin solution. If that is not feasible, you may have to abandon this feature. Sorry!
EDIT: Actually, after using a better search query, here's a Java solution that seems to support this through partitioning the initial file: JumpLoader. Here is the documentation page for resuming downloads. Best of luck! (You will note that there are purchase links - this is only for an unbranded version, and for the source code. You can use the JumpLoader branded version for free.)