It would be nice if we could arrange for people to be able to hang up the
   phone for long periods -- at least 24 hours, and preferably arbitrarily long
   -- without losing their TCP connections.  Does anyone reading this know by
   what mechanism the loss of PPP connectivity is detected?  Would it be hard to
   modify the NetBSD kernel to disable this mechanism?

The kernel will drop a TCP connection after a certain number of retransmission
failures.  Look in sys/netinet/tcp_timer.c for the code which does this.
Increasing TCP_MAXRXTSHIFT and expanding the tcp_backoff[] array would allow
you to disconnect for a longer time.