It's *POSSIBLE*, yes - I can think of a scenario or two that would let
it happen, but can't say for sure if the one I'm about to offer is true
for your vehicle (year, make, and model of which you don't bother to
mention, so we're stuck going on ESP to try and help you...)

Consider a water pump whose impeller is, under ideal circumstances, held
tight to the shaft by a bolt into the shaft, or a nut onto the shaft.
Consider said nut or bolt somehow backing off - not completely, but
enough to be loose, perhaps permitting the impeller to spin free of the
shaft - but only when it "backs straight away", rather than getting
tipped - When it moves to a tipped position, it spins with the shaft,
and for the most part, acts as it should - namely, moving water thorugh
the system. But when it gets into a "straight" position, instead of
turning the impeller, the shaft simply spins inside it, leaving the
impeller stationary, and moving no water.

Presto... Intermittent water pump...

Same concept could be happening on the pulley side of things - replace
"impeller" with "pulley" everywhere in the paragraph above, and you end
up with the same thing happening.

Either way, your junk Autozone pump is a "lifetime" unit, so go get a
new one and replace it. Not too difficult, eh?

(And for the record: About the only thing I consider Autozone good for
is name-brand oil and brake pads, and I consider the brake pads dodgy,
at best. Overall, and in my opinion, Autozone blows syphyllitic goats in
almost every other category.)

I once bought a 1966 Plymouth with a 225 slant six. It had an overheating
problem that I traced to the water pump impellor slipping on the shaft. It
was a press fit. There may have been more slip at different engine
temperatures and speeds than others, I can't say for sure. If it were true,
though, that water pump could have been considered intermittent. Anyway, the
slip was obvious when spinning the impellor by hand - with the water pump
off the engine, of course.

Never heard of one getting intermittent. That doesn't mean it's
impossibe but.... it's not likely.

The 'pumping' part of the pump is an iron impeller pressed onto the
waterpump shaft.
They don't wear out.
The reason pumps get changed is mostly the shaft seals fail and they
start leaking.
The shaft bushings (or bearings) are place outside the seals so when
the pump starts leaking ot can affect the shaft bearings and cause
the pump to make noise.

You may have a hose that is collapsing and not letting the water pass
thru.

Heater cores will also get stopped up from rust and scale deposits
that break loose and travel with the water to the heater core.

Buy a 'quality' thermostat.  I tried several of those 'cheap' ones
made south of the border (wherever the heck the border is) and they
all failed within a years time.
They 'look' good and the price is right but I'd rather spend a few
dollars more and not have to take the crappy things out and do the
job all over again next year.

Never heard of one getting intermittent. That doesn't mean it's
impossibe but.... it's not likely.

The 'pumping' part of the pump is an iron impeller pressed onto the
waterpump shaft.
They don't wear out.
The reason pumps get changed is mostly the shaft seals fail and they
start leaking.
The shaft bushings (or bearings) are place outside the seals so when
the pump starts leaking ot can affect the shaft bearings and cause
the pump to make noise.

You may have a hose that is collapsing and not letting the water pass
thru.

Heater cores will also get stopped up from rust and scale deposits
that break loose and travel with the water to the heater core.

Buy a 'quality' thermostat.  I tried several of those 'cheap' ones
made south of the border (wherever the heck the border is) and they
all failed within a years time.
They 'look' good and the price is right but I'd rather spend a few
dollars more and not have to take the crappy things out and do the
job all over again next year.

 Much more common: a collapsing lower rad hose. When the water flow
speeds up as the pump drives it through the system, the pressure in the
lower hose drops (Bernoulli's Theorem) and an old, soft hose can
collapse and restrict the flow. My Dad once replaced the pump two or
three times before his brother came along, revved the engine and
pointed out the lower hose squeezing itself shut.
    That's why many replacement hoses had springs inside them.
        Dan