It would be useful to know how you metered. Do you have the Pentax TTL prism
with the built in meter, were you using a separate hand-held meter, or were
you guessing based on Sunny 16 or something like that? Also, are the blank
frames adjacent to each other or are they scattered randomly throughout the
rolls? If adjacent, are they at the beginning, middle, or end of the roll?

Apart from the always conceivable but extremely unlikely possibility that
you left the lens cap on for the blank exposures, this sounds to me more
like an operator exposure error than a camera problem. There isn't a whole
lot that can go wrong with a Pentax 67 camera that would lead to some
properly exposed negatives and other totally blank negatives on the same
roll.  I'd guess that you grossly underexposed the blank frames for some
reason, maybe just a metering error on your part, maybe failure to properly
set the shutter speed or aperture where you intended to set them, maybe
inadvertent movement of the film speed dial to an excessively high speed
(not too likely unless the blank frames are all at the beginning or end of
the roll),  or conceivably there's a problem with whatever meter you're
using that's causing it to operate inconsistently.

To check the TTL meter if that's what you have, put the camera on a tripod
and point it at an area such as a wall, a large piece of mat board, anything
that isn't overly bright or dark.  Set the aperture and shutter speed for a
correct exposure, look through the viewfinder, then while looking through
the viewfinder open and close the aperture a stop at a time.  Then leave the
aperture at one setting and increase and decrease the shutter speeds a stop
at a time. Does the needle consistently move in the right direction by
approximately the same amount with each change of the aperture and shutter
speeds? If so then set the aperture and shutter speed for a correct exposure
and while leaving them at that position increase and decrease the film speed
a stop at a time. Does the needle move properly as the film speed is
increased and decreased? If you're using a hand-held meter then you can do
the same thing with it, just see how the meter indicates exposure changes as
the aperture, shutter speed, and film speed settings  are changed. If  the
indicated exposures aren't consistently changing as they should with changes
in shutter speed, aperture, and film speed then you've probably found your
problem.

If the meter looks like it's operating properly then the only other
mechanical thing I can think of is some kind of malfunction of the mirror so
that it was never moving up out of the way as the blank frames were made.
You might try locking the mirror up and then looking through the viewfinder
to make sure you can't see anything (i.e. that the mirror has in fact moved
up). Also make an exposure without the mirror locked up while looking
through the viewfinder, see if there's the moment of darkness as the mirror
moves up and then back down.

If these tests don't indicate a mechanical problem then short of leaving
the lens cap on I can't think of any reason other than exposure errors on
your part why some frames would be properly exposed and others would be
blank on the same roll. Maybe somebody else can.

Assuming you didn't goof in some other way (lens
cap, exposure), your camera is clearly malfunctioning.
Get it fixed.

Did the shutter actually fire? It's fairly obvious
when it does on a 67.

I would have shot a roll or six at home before taking
a new camera in to the field. Fewer surprises that way.

Laura Halliday VE7LDH     "Que les nuages soient notre
Grid: CN89mg                    pied a terre..."
ICBM: 49 16.05 N 122 56.92 W       - Hospital/Shafte

Sounds like it's time to get the camera to a repair shop for a check up. I
would recommend this for any camera bought sight unseen. Assuming no
operator errors, there's clearly a mechanical problem, most likely with the
shutter. Can you open the fim back and look through the lens from the back
while you shoot a dozen or two times; this would confirm the shutter is
indeed opening. (Use a slow shutter speed and point toward a light
surface.)

Thanks to all of you for your responses. FWIW the cap was not on the lens.
The un-exposed frames were in no particular order. Very random. I shot
everything metered through the TTL prism. Here's what I've learned since I
posted here yesterday:

I just got home from visiting with my camera guy. So far we've been able to
determine that when the camera is in mirror lock-up, the lens mounted and
the back open, the shutter "fires", but the curtains don't separate. No
light is visible through the shutter curtains.

With the lens removed, the mirror locked-up and the back open, the shutter
appears to be working as it should.I can see light coming through the lens
and the shutter curtains.

When we set the mirror lock-up lever and the mirror achieves lock-up, there
is a small barely audible click after the sound of the mirror locking up.
I've been told this is the body telling the lens to set the correct aperture
I selected in preparation for mirror lock-up photography. It's at this point
that we believe the shutter is mall-functioning.

Any ideas? Anyone experienced anything like this?

FWIW most of the exposed frames were properly exposed. And yes, I did
consider operator error, on account of I'm kind of an idiot sometimes, but,
I'm confident operator error is not an issue. This time ;-)