Auto save is not possible yet but there is one thing that you can do to extract all attachments that you got in iMessages on iOS.
Connect your device to pc, and make full backup.
Than use this or some other software to extract backup
Code:
http://supercrazyawesome.com
You should look in backup for iOS files (last in list)
and after you have extracted data, check this out in dir where you have extracted data:
Library/SMS/Attachements
And after that you will have it all but organised in many sub dirs and each of them contain your multimedia attachments.
This can be done even on devices that are not jailbroken.
Only thing that i cant figure out is how to extract all pictures from this many sub dirs into one folder. Anybody have solution?