There is no getting away from the fact that all natural fibre ropes, when used in a damp or wet environment, will eventually rot through. However, choose the right rope for the job and it could be lasting 10 years, probably as long as the posts supporting it. Don’t forget that the synthetic ropes which are made to look like natural fibre, and are usually made from polypropylene, will often suffer quite badly from the effects of ultra-violet rays in sunshine and may not last any longer than 10 years.
My choice for an outdoor rope would usually be Manila and, as mentioned above, it is not unusual to hear of a 10 year life span when using something like 32mm Manila to support your roses. As it is the damp that leads to the problem it is impossible to give a guarantee, do you live in a wet location with lots of fungal growth or a dry one? If your garden gets lots of rain but also good drying winds then your rope could be nice and dry for much of the year. If you are supporting the rope by passing it through holes in wooden posts then the place the rope gives way is usually at the posts – where its stays damp within the hole.
If you decide to use something like Flax or Hemp outdoors then the rope is likely to have a very short, useable lifespan. I have heard of it lasting just 1-2 years, rarely more than 3.