Quick answers
Can an old bitumen membrane be patched, or does it have to come off?
If it is still stuck down and only seams or corners have opened, it can be repaired locally. If it has come loose, blistered or wrinkled over a large area, it all comes off before anything new goes on.
A bitumen membrane protects the roof only as long as it stays stuck to the slab. Over the years the sun wrinkles and cracks it, the seams open and in places it comes unstuck. From then on water doesn't stop at the surface: it gets underneath and runs freely between the membrane and the slab.

On this roof the old membrane was full of patches, and once stripping started it rolled up like a carpet, because it had already come away. One more patch wouldn't have solved anything. It all came off, the surface was cleaned and the white waterproof coating went straight onto the slab. The same was done on a terrace beside a tiled roof, where the membrane was also stripped from the walls under the roof tiles.
The reason is simple: new material laid over a membrane that has come loose has no solid base. It will hold only as long as the old layer underneath holds, and any water already trapped there has no way out.
That doesn't mean every old membrane has to go. On another roof the membrane was still stuck down over most of its area. Only the pieces that had lifted were cut out, and the seams and parapets were sealed. To know which case you're in, someone needs to see the roof up close, walk it and check where the membrane has come away.
Jobs that show it

Old Bitumen Membrane Stripped and Replaced with a White Coating
A roof's old bitumen membrane had wrinkled and come away. It was stripped off completely and the roof was coated with white waterproofing, including the low walls under the railings.
See the job step by step

Terrace Beside a Tiled Roof: Old Membrane Out, White Coating In
The old bitumen membrane had torn and come loose. It was stripped off, and the terrace and its walls were covered with a white waterproof coating.
See the job step by step

Membrane Roof: Sealing the Seams and Parapets
The membrane had torn at the edges and its seams had opened. The loose pieces were removed, and the seams and parapets were sealed with a white waterproof coating.
See the job step by step