In a book about "Harmoniums" or reed-organs I read about the repair of
reeds (for an organ that operates the American way: the reeds are
powered by "compressed" air):

    New reeds have to be produced, using the original as a master. This
    is a difficult job. Using the broken reed one can produce a new one
    from a strip of spring-hard (Correct word??) brass. If the brass is
    not hard enough, it can be hardened by hammering it carefully. The
    thickness of the brass should be corresponding to the original,
    otherwise is should be machined. Many reeds do not have an equal
    thickness from top to end, so a lot of craftsmanship is needed, an
    not seldom one has to start over again.

In another book I read about manufacturing reed:

    Use a strip of soft brass.  Using a small rolling machine (as
    jewellers do often have) you can modify its thickness. Alternatively
    you can hammer it down to the wanted thickness. If the brass gets to
    hard, you should glow it out. Always produce a strip slightly bigger
    as needed, taking care the strip stays straight. Cutting of a strip
    from the brass plate is best done on glas, carving it with a knife,
    and breaking it of. Never do use scissors, since the strip will not
    stay straight. Put the strip between two strips of hard wood, in
    order to file it to its definite size. If the thickness of the strip
    has to be modified partially, it comes to patient and carefully
    filing and grinding by hand

Regarding this, the best way to work around the problem is to buy
replacements.  If no good replacement can be found, it is possible to
order new reeds from specialized firms. However, this easily will turn
out to be a costfull way. One also could contact organ building
companies, since organs do have reed-registers, so they will know how
and where to get new ones. In Europe very often builders of church
organs also did (ans some do) produce reed organs.

Nowadays a certain revival of the (European) reed organ can be seen.

By the way: the American reed organ is operated by air pressure, the
European type uses vacuum. The advantage of the American system is
that is produces a bigger sound. The European type however is much
easier to build and service, since its construction is far less
complicated, and the reeds can easily be tuned.