The name is Gear, Richard 'High Maintenance' Gear and believe me, I feel for your peeling seam tape, who wouldn't?
You really have a choice here, either use a professional outdoor clothing repair specialist who should be able to reapply heat-activated seam-sealing tape to your clothing.
Scottish Mountain Gear for example - www.scottishmountaingear.com - can repair Gore-Tex waterproof clothing using genuine Gore-Tex fabrics and tapes.
Update Lancashire Sports Repairs also offer a re-taping service and will either retape the entire jacket for £40 or for £25 will re-tape just the hood, shoulders and neck. More details at www.lsr.gb.com.
Alternatively, you can try to do the job yourself. Point North - www.profabrics.co.uk - sell iron-on sealing tape suitable for both PU and three-layer waterproof garments which you can apply yourself as does Pennine Outdoor - www.pennineoutdoor.co.uk.
Make sure you clean the garment and degrease the seam area thoroughly before applying and you should be good to go.
If you have only small areas of peeling tape, you may be able to stick them back in place using a seam sealing product like Seam Grip. Don't worry about breathability by the way, most if not all original seam tape is non-breathable, which is one fo the reasons that large manufacturers have gone over to micro-tape.