How to resume a Mavericks download on OS X 10.6?
It's a usability bug. You have to open the App Store, log-in, and only then will the Resume option work. To resume, you can also click "Download" on the OS X Mavericks line in the Purchases table of the App Store.

Since there's no instant feedback as to whether anything is being downloaded unless your connection is very fast, you can use Activity Monitor to check whether network download seems to be saturated. An alternative is iStat Menus (non-free with 14 day free trial). There, you can not only see that data is downloaded, but you can confirm that it is the storeagent process that does the downloading.