As someone else in the northeast who loves all things stone, I have to
agree.
Any repair involving mortar or concrete is likely to suffer from
freeze/thaw
and break up in fairy short order. You can try hammering out enough
concrete
to get bricks or concrete pavers (preferred; bricks get SLIPPERY in
winter) on,
but again the mortar that holds them together will be a challenge to
keep
intact for long.

For short term, try breaking some concrete off and putting a fresh
coat
on with sealer. It may last at least a while. Long term, jackhammer
the
whole thing up and start again with what you want. I used granite
slabs
resting on compacted earth. My grandkids will be able to visit them.

Thanks. Sounds indeed like freeze/thaw cycle is working against me!
Many other houses in my project still have the original steps intact
(no carpet). I believe my carpet retained moisture (it was always
wet) and ended up causing the concrete underneath to crumble and break
off on the steps. Unfortunately, jackhammer and start from scratch is
not a (cheap, anyway) option: the steps are poured and form the upper
walls and ceiling of the cold-storage room underneath, extending out
from the foundation. If the steps were the cheap pre-cast variety,
jackhammer would work, but not in my case alas.

A couple of people have recommended building wooden steps and porch on
top of the ailing concrete, either using pressure treated or cedar
($). Not sure wooden steps would match the front of the house (all
red brick), maybe if painted with a reddish stain. Might be the way
to go, though I may try to put some patches on and see how long they
last...

Cheers.