Both programs you mentioned already do this. However, once you upload the file somewhere else, you cannot prevent the server from removing album art again, if it decides so.
Also, ID3 tags are a finicky beast, and it could be that the server doesn't recognize the specific format you're trying to use:
Try different image formats – JPEG vs. PNG;
Use iTunes or foobar2000 to convert the ID3 tags between different versions (e.g. iTunes writes ID3v2.4, but quite a few tools only support v2.3);
Use mp3Diags to make sure the ID3 tags aren't corrupted (though note that it sometimes gives false positives for v2.4).