My phone occasionally tells me: "Currently unable to continue download, please try again later". What was it trying to download?
I have read in several websites that users with the Samsung Galaxy S3 are getting that exact same message when having MMSes that fail to download (probably old ones...).
If possible, delete all and repeat the steps taken to get the message. If you don't get the message, the problem is solved and in the future we all know from where it is comming.
My original comment on the question:

Further into that issue, other users of your device have reported the same message in relation to the MMSes. Do you have any MMSes on your device?