Amending my prior comment: I stand by the two suggested work-arounds, but retract my theory that the problem has to do with how many TCP sockets are in TIME_WAIT.
If you google "autofs TIME_WAIT" and "autofs nfs bindresvport address already in use" and "autofs can't read superblock" (the latter two being two of the errors that show up in the syslog), you'll find various discussions, going back a few years, on this problem of errors when doing lots of automounts in rapid succession. But as far as I can tell, no discussion ended in a definitive explanation and bug fix.
Amending my prior comment: I stand by the two suggested work-arounds, but retract my theory that the problem has to do with how many TCP sockets are in TIME_WAIT.
If you google "autofs TIME_WAIT" and "autofs nfs bindresvport address already in use" and "autofs can't read superblock" (the latter two being two of the errors that show up in the syslog), you'll find various discussions, going back a few years, on this problem of errors when doing lots of automounts in rapid succession. But as far as I can tell, no discussion ended in a definitive explanation and bug fix.