There are plenty of coders in their 60s, I'm one of them. You don't think computer programming was invented in the dot com boom do you? I have colleagues still coding who are in their 70s.
And no we aren't all coding in Cobol or Fortran 4.
I do agree though that it would be difficult for most of us to get new jobs in another company as developers because of the age-ist behaviour of many of our younger colleagues.
I guess your 22 year old founder of a trendy Bay Area startup would have a problem hiring a 60 year old but that's both silly and illegal. I'm not sure trendy Bay Area startups attract the 60+ crowd anyway.
I don't think we'll know the answer to the age question for a little while. The number of coders has been growing over time, so the potential pool of seriously older coders (60+ for sake of argument) is already small to start with.
Anecdotally, three very different examples:
my mother (71) stopped coding in 1969
Guido van Rossum (60) is still coding
Darryl Havens (61) is Distinguished Engineer at Amazon - not per se a coding role, but definitely an engineering role
Coders? Never.
Interview for medical job: Normal
Coders?: Often humiliating