"muffled thump"  Could be you have a thrown belt on the balance shafts.
Trully mysterious.
Pull the cover off the timing belts and see if everything is in place.
If you have over 40000 miles on the belts you need to change them.
The cam belt may have jumped a few notches and threw the valves out of
timing.  This would make the engine run stangely.

YES - check the main computer!! Tap the case and see if it helps.
My 1987 944 car also ran intermittently like you said...run then stop then
surge ahead...didn't start, sometimes ran perfectly, etc.

It was the BRAIN - I resoldered the larger internal connections.

I've got a 944 turbo with a problem I think I just solved
(see my post '86 944T - Runs at idle speed only when cold?),
but I had to research some similarities with the 944.  Your
problem might be related, and here's something you might
want to check - it's an easy test.  

The Throttle Switch in the 944 NA (and 944T) tells the DME
when the driver lifts his foot off the accelerator.  If the
RPMs are high and throttle is closed (trailing throttle
condition) , the DME shuts off fuel to save gas.  My switch
was bad.  If the switch fails open it tells the DME the
throttle is open, and it will run fine, but use more gas.
However, if it fails closed, or if bits of the switch were
to rattle around and occasionally short the connections as
you were at speed (RPM>1600) it would suddenly shut off gas.

Perhaps it's a long shot for you that your switch is
intermittently shorting out, but when I tested mine, it was
very flaky, occasionally shorting when I snapped the
throttle closed, occasionally staying open, occasionally
staying closed even when the throttle opened.

You may need to check for your model, but on mine, the
throttle idle sensor switch went to pin 2 of the DME plug
(take off plug, measure with ohmmeter to ground should be
less than 10 for throttle closed, open for throttle open).  

You can also access it for testing at the switch itself -
for my 944 T it's on pins 4 and 6 of the switch.  The turbo
also has a throttle position sensor (potentiometer) that is
integrated into the switch (pins 1-3) that is not found in
the NA.

You should be able to just disable the switch and drive it
around for testing,  if your problem is intermittent.
Search in the "944 shudder" for more info.