How to repair mortar that is crumbling

I've no experience of lime mortar, but I would work under the same assumptions as I use for plaster and normal mortar.

That is, when removing the loose material go a little way into the sound areas, but don't be too aggressive.

So in this case I'd start with a steel brush to get the really loose material out and then use a chisel (or an old long screwdriver) to scrape away a little bit further and test out the remaining mortar to see how loose and crumbly it is.

If you find that you are removing a lot of mortar then I'd start to get concerned, but if you only do a small area at a time you shouldn't affect the stability of the wall.

It might be useful to get a couple of people in to give you quotes for the work. They should explain what they would do and give you an indication of just how bad the mortar is. Ask them if there could be structural problems when repointing - it's a perfectly valid question.

Just don't tell them you intend to the work yourself :)

It is not so much about mortar as it is about the working process. You should clean out the old crumbling mortar to make place for the new one. Remove the old mortar so that all parts are firm and nothing is crumbling - you can even scratch out a bit of the old mortar. The very important part is to wash the wall properly with water so that all parts hold firm and there is no dust - otherwise the new mortar would just fall out. Than press the new mortar in the joints and fill them, make them smooth on surface.

As for the mortar the lime content should not be important for the lifetime, but you can add a bit for better workability. Generally there should be no or very little lime in a stone wall. The new mortar should consist of 1 part of portland cement and 2-3 parts of sand.

If you do it properly (well prepared surface, good mortar), the new mortar should not crumble or dust for tens of years.

A personal experience: it is a very time consuming monotonous work, but the result can be very good if done with care.