A damaged log database can prevent DropDMG from launching or cause it to crash or report internal errors. Database damage can be caused by crashes or disk errors.
If you have a backup from before the damage occurred, you can quit DropDMG and replace the file:
/Users/<username>/Library/Application Support/DropDMG/Log.dropdmglog
with a working copy. See the How can I open the Library folder? section for how to find this file.
Otherwise, you can delete the Log.dropdmglog file and DropDMG will create a new one.