In reply to Tall Clare:
> If you have access to a normal sewing machine [...] set the machine to do wide-but-close-together zigzag stitch
A sewing machine would be nice, but considering the OP is talking about applying patches to a down jacket, using a sewing machine is going to be a bit tricky without dismantling the down enclosure, or sewing through the entire down compartment...
To the OP:
I'd suggest applying patches with rounded edges, to minimise exposed points that are easier to peel off.
If the jacket has a self-fabric stuff sack (i.e. made from the same material as the face), apply a tape patch to that, and put it through a representative wash; i.e. do a test.
DWR treatments alter the surface properties of a fabric, and may well stop the tape sticking
For peace of mind, simply hand-sew a simple, angled running stitch around the edge of the tape (sew into the fabric outside the tape, bring the needle back up to the surface on inside the tape perimeter, repeat). Once washed, you could remove the stitching, I guess, if you feel it looks a bit rubbish. How often do you intend to wash the down jacket...?