Just an idea for a manual workaround, that may not be helpful in your situation:
0) You start with your original extract, which you should have in a twb file, so that you can switch back to your original live connection at any time.
1) You have your extract saved separately as a tde file, and open it directly from Tableau to generate a new extract based off your original, with filter leaving out the dates for which you want your data refreshed. Save this new extract as a separate tde file, you will be adding rows to it later - essentially this contains only the "old" data, that will be left intact.
2) Open your original twb file (from step 0), switch to live connection and generate a "new" extract filtering ONLY to the dates containing the new data - this is what you need to add to the file from step 1.
3) Open your extract containing the "old" data in Tableau. Although it is an extract, you will have to tell Tableau to make an extract out of it once again to activate the "Extract" submenu in the File menu.
4) Go to Extract->Append Data From File... and point it to your extract from step 2 containing the "new" data only.
You end up with an extract that contains your "old" and "new" data.
Not sure if this helps at all though, as:
1) It is entirely manual process, very prone to errors. Probably some of the gurus could help you figure out if you can automate this via tabcmd, but to the best of my knowledge, there is no way.
2) You are creating your "old" extract out of extract, but still essentially this wrangles the entire available information, so I do not know if it will be faster than referring to the original datasource to make a full refresh.
This solved my doubts.