Fixing your expensive technical fabric clothes DIY stylee
Introduction
By now we've all been there, we've bought an expensive waterproof jacket, a pair of paints or waterproof overshoes. They are all fantastic and reasonably waterproof when well maintained, but there comes a time when they all fail in the same way. This failure all have one thing in common and those are the seams.

The seams on waterproof "tech" fabrics like Gore-Tex are all sown in the classic fashion, but are then covered with seam tape so that water has no chance to pass through the needle holes and layers of fabric into the dry side of the garment. With time and continuous rubbing while wearing this seam tape fails and let's go.

These failures come in two ways, either the seam tape lets go completely or the seam tape separates from the glue layer, leaving an opaque white layer behind. The first option has a chance of being fixed using the process below, but the second one needs new tape.
Obtaining seam tape is not easy, there's no webshop on the internet that sells seam tape of the right kind, but there is an old school machine company in one of the old fashioned UK fabric cloth areas that sells the tape in small quantities. West Bridgford Seam Tapes on Amazon sells the (near?) exact same tape that clothing manufacturers use and which I used.

Whether applying new tape or trying to re-apply existing tape you need the following:
An iron (you know, the electric thing you use for ironing clothes) with working thermostat and temperature setting
A small(ish) piece of baking paper
A (small) wall paper (seam) roller

How to setup your iron

Warm up your iron on the lowest setting
Find an out of sight, less important piece of seam tape (or perhaps a location where just a bit of tape glue is visible)
Put the baking paper over the seam and the iron on top of that for a few seconds
Remove paper and iron
Quickly check if the glue got fluid (it looks like the tape started sweating a bit)
If not, increase the temperature put back the baking paper on the seam tape and try again
If it is possible to move the tape around in the glue, the iron is hot enough
If anything moved, fix the alignment of the tape back to original while the tape is still hot

Make sure that the lowest temperature is not already to high, so be careful!
How to (re)fix a length of seam tape
First get your iron up to temperature using the setup guide above
Cut the seam tape to the length of the seam you want to fix or use the existing tape
Cut/shear/rip a piece of baking paper to cover as long a piece of tape you can keep in place with one hand. On a curve this is about 10cm, in a straight line maybe 30cm?
Cover the length of seam you want to cover with tape with baking apper on top. Keep the whole length under slight tension, without any ripples or folds in the fabric, tape, paper.
Make sure the seam is in about the middle of the tape.
Put the tip of the iron on the paper covering the area where the tape is below. Move slowly along the tape maing sure that the paper is covering the tape and the tape is covering the seam
Fix any errors in covering the seam with the tape as soon as possible, check regurarly for proper alignment
When a length of seam has been covered, roll the tape firmly on to the fabric using the wall paper roller
The result should look something like the image below

What you don't want to do is to cover your iron in glue, that's why the baking paper is highly recommended

Disclaimer
I haven't tested the garment I fixed in this way for waterproofness yet, just for adhesion of the tape. No guarantees. No warranty implied or offered. YMMMV. If you ruin your expensive garment by following my experience, it is your problem ;-)