I attach a sample program test.el whose central function, test-slave,
invokes wget asynchronously before waiting for the process to exit.

The issue I'm facing is that running test-slave twice in succession,
each time in a new thread, causes accept-process-output to hang with no
output (unless a timeout argument is given, in which case the function
returns nil) the second time around.

When this happens, the process sentinel is never called, which is why
I'm assuming accept-process-output is indeed "hanging" in some sense and
it's not just that the process has already exited and so has no further
output.

I could very well be doing or assuming something incorrectly, but what
baffles me is that the "hang" does not occur either when Emacs is run
non-interactively, or when "https://en.wikipedia.org/wiki/Emacs" is
replaced with "https://www.gnu.org/software/emacs/", or when test-slave
is run in the current thread (and not in make-thread).

Since I can reliably reproduce this on both an optimised build of master
and a non-optimised build of emacs-26, I hope to be able to provide
further insights using gdb as time allows.  Please let me know if there
are any specific details/output you would like me to provide.  As a
relatively inexperienced gdb user I welcome any tips and tricks for
debugging threads and processes.

Here are some ways test.el can be run to illustrate the issue:

# All five processes exit successfully.
emacs -batch -l test.el -f test-no-threads

# All five processes (and threads) exit successfully.
emacs -batch -l test.el -f test-threads

# All five processes exit successfully.
emacs -Q -l test.el -f test-no-threads

# First process and thread exit successfully,
# but accept-process-output starts timing out in second thread.
# Warning: may leave empty wget-log files lying around.
emacs -Q -l test.el -f test-threads

Details of the two Emacs versions I'm using follow:

In GNU Emacs 26.1.50 (build 2, x86_64-pc-linux-gnu, X toolkit, Xaw3d scroll bars)
 of 2018-10-11 built on thunk
Repository revision: a7ebc6bf633bd3849ccab032dad6b1fd31b1ef43
Windowing system distributor 'The X.Org Foundation', version 11.0.12001000
System Description:	Debian GNU/Linux testing (buster)

Configured using:
 'configure 'CC=ccache gcc' 'CFLAGS=-O0 -g3 -ggdb -gdwarf-4 -pipe'
 --config-cache --prefix=/home/blc/.local --program-suffix=26
 --enable-checking=yes,glyphs --enable-check-lisp-object-type
 --with-mailutils --with-x-toolkit=lucid --with-modules
 --with-file-notification=yes --with-x'

Configured features:
XAW3D XPM JPEG TIFF GIF PNG RSVG IMAGEMAGICK SOUND GPM DBUS GSETTINGS
GLIB NOTIFY ACL LIBSELINUX GNUTLS LIBXML2 FREETYPE M17N_FLT LIBOTF XFT
ZLIB TOOLKIT_SCROLL_BARS LUCID X11 XDBE XIM MODULES THREADS LIBSYSTEMD
LCMS2

In GNU Emacs 27.0.50 (build 21, x86_64-pc-linux-gnu, X toolkit, Xaw3d scroll bars)
 of 2018-10-11 built on thunk
Repository revision: 5bd8cfc14d4b0c78c07e65a583f42a10c4cbc06d
Windowing system distributor 'The X.Org Foundation', version 11.0.12001000
System Description: Debian GNU/Linux buster/sid

Configured using:
 'configure --config-cache --prefix=/home/blc/.local --with-mailutils
 --with-x-toolkit=lucid --with-modules --with-file-notification=yes
 --with-x 'CC=ccache gcc' 'CFLAGS=-O2 -march=native -pipe''

Configured features:
XAW3D XPM JPEG TIFF GIF PNG RSVG IMAGEMAGICK SOUND GPM DBUS GSETTINGS
GLIB NOTIFY ACL LIBSELINUX GNUTLS LIBXML2 FREETYPE M17N_FLT LIBOTF XFT
ZLIB TOOLKIT_SCROLL_BARS LUCID X11 XDBE XIM MODULES THREADS LIBSYSTEMD
JSON LCMS2 GMP

Thanks,

-- 
Basil