Very well said, +2!
Get one of those containers of the jewellery soaking cleaners. Drop your band in that once every 3-6 months (figure you'll just rinse it with water on a regular basis right? That'll get most of the residue.
That way, any sweat that builds up as "gunk" will get eaten up by the jewellery cleaner.
Had a link I wore all the time years ago that I did that with. Always amazed me how much could accumulate between the links (a little disgusting)
It should go without saying - remove the watch from the band before dropping it in the jewellery cleaner.