To properly support the jack, apply foam tape to gently press the jack into position, like 3M foam tape.
Most vinyl electrical tape these days uses really crappy adhesive, with the exception of 3M. The competition just celebrated the 2008 Olympics, if you get my drift. I hate the thought of your Sansa full of black goop.
For the “non-technician” repair, shall we call it, a wee dab of that conductive solder preparation (Solder 5?), on the solder pad / connection, followed with a bit of foam tape to support the jack properly against further damage, should last for years.
If you don’t have some proper foam tape, a small wad of the foam wedges used for makeup will do. If you sneak this bit of foam from your wife or girlfriend, get her a replacement.
In any case, don’t tell her that the missing bit of foam was chewed off by a mouse, as she may start screaming and running about, and the newly repaired Sansa in your hand will quite possibly be dropped to the floor! Be careful!