How long do speakers last?

The older a speaker is that much better it will sound, but Capacitors and surrounds will deteriorate in time, if they are good rubber surrounds on the woof's this will not be a problem really, but would still suggest replacing caps for another level of performance, not really because they are necessarily failing, although they do, but newer caps are far more advanced and better material, (with musical results not just scientific results) now available than anytime 10-20 years ago. Beyond that if you do not toast a voice coil or damage them they could last more than a lifetime as long as the glue on the cabinet don't let go, or the wiring does not corrode to some crazy point.

The Reverend Billy Graham has been a speaker for over half a century... :-)

That's an old speaker...

Once I had clipping problems (5 seconds) but it sounds OK. Did that damage the speaker?

Can any good audio repair shop refurbish these speakers?
Or should I bring to speaker rebuilder? (I live in Los Angeles)

You could contact DCM directly and get heir advice. Their phone is 877-326-5683, or thru their website:

www.dcmspeakers.com

I'm sure they still work on older speakers, You could perhaps just send them the drivers for rehab. I'll bet they can even sell you a new grill/sock.

It depends on the material and the enviroment.
Here is a pdf file on Rubber Products: Recommended Shelf Life
See Table I on page 5 for type of rubber, common or trade name and the shelf life.