One can take off the padding and pop it into the dryer on "air fluff" setting for a few minutes. This is what my Ironrite manual recommends for padding that has compacted.
The type of padding used for Ironrite ironers, and indeed all rotary ironers (then and now), along with ironing board pads is called "knitted cotton". It is VERY difficult to find outside of suppliers for commercial laundry rotary ironer's. Even then it will probably come in widths greater than your Ironrite, thus would have to be cut down to fit.
You can try searching various textile suppliers for commercial laundries, and see if they have knitted padding, though many laundries have moved onto Nomex and other man made fibers instead of cotton.
There is lots of vintage NOS Ironrite padding out there, however it usually goes for dear sums on eBay and other such places, but then again you may turn up a deal at estate sales or even a member here in the group. Often persons selling on an Ironrite will have NOS packets of covers and or padding as well, however have usually found such sellers want to sell the things as a job lot.
Another option would be to purchase roller padding for the larger Miele rotary ironer, and cut it down to fit, using your current pad as a guide.
One thing to remember, NEVER launder knitted cotton padding in water. It will shrink and distort, thus will not fit your ironer properly again.
Oh yes, knitted cotton padding was also sold as "silence" under padding for dining room tables.
Launderess