I'm guessing that the siding is a T-111 style, but the boarding is made up of some pressed paper type material rather than the normal plywood T-111. If this material gets wet it just absorbes the moisture, swells up and rots. The only way to reapair it is to cut out the bad sections and replace them. The problem is that if the damage is along the bottom as you say it is, there is no easy way to match up to the existing siding.
One suggestion is...if the damage doesn't go too high up the wall (mostly just under the skirting) could you cut out the bad parts and replace with plywood and then install skirting that goes a little higher up and covers the repaired section?
Another way, and I'm not too sure of how it would look, is to cut out the bad parts, put in replacement plywood or pine boarding and go all around the home with this new wood so that it looks like a trim piece. Then put the skirting on.
I am trying to think of an easy method that will look good and not be too expensive, but the only perfect method is to replace the damaged panels from the skirt level right to the roof line because patching the panels and making things match will be nearly impossible.

I have the same issue in a 1988 Redman MH.

As a Project Manager for a Development/Construction company, maybe I can help.

The panels you refer to are MDF (medium density fiberboard) and were used prior to the 1990's in both flooring and exterior wall coverings for manufactured homes. This material, unless treated with a satisfactory primer, will be subject to damage from moisture rather easily. It is a HIGH maintenance material.

To deal with the crumbling (it is generally not rot) caused by the invasion of moisture, it is best to cut out those areas that are damaged and replace with construction grade OSB (oriented strand board). It is cheaper than plywood, is more structurally sound, and won't delaminate like layered-panel material such as plywood. Wood putty and caulking might fill the small areas, but the damage goes further than what you can see. If you have a 6" area of damage, you should cut out at least 18" in all directions.

Be aware that, if you simply replace the siding with plywood, OSB, or T-111, you will probably not be matching the existing texture of your current siding. Painting it will make it look good from a distance, but the difference in the material will be obvious. You may want to consider covering everything with a different material.

As I said, I'm facing the same problem. My solution, since the damage is only where the siding meets the stucco skirting, is to cut out 16" above the skirting, all the way around the base of the home, then replace it with 7/16" OSB. I'll be applying a polyethylene (rigid plastic) faux stone from the bottom of the skirting, overlapping the OSB and the MDF (about 48" high) as a wainscot. Above that, since the MDF is still intact, I'll be applying faux vinyl logs. These are foam-filled and apply just like regular vinyl siding.

Be careful when cutting the old siding off. You can use a circular saw, but set your blade depth just slightly less than the thickness of your MDF, so you don't cut into any studs, and heaven forbid, any electrical lines.