Perfectly running 2002 Avalahche 110k miles 5.3 4wd with engine at 3000RPM on highway misses as if about to kill then works fine for 20 miles or so.... recently changed oil and air filter. Could it be Bad gas?, bad fuel filter? This started happenning after battery went dead from car being stored without running for 4 months and putting a new battery. Could it also be injectors being gummed up from lack of use?

Radiator cooling fans not working? The ECM is protecting the engine by shutting it down.

Sounds like you have a misfire in the engine. Do you have a check engine light on?

Have an electronic evaluation carried out, it's quicker and in the long run safes you frustration and cash.

If one of the engine components is acting up, you should get a check engine light and have codes for the components. If the light is not coming on, it could be a suspension or mechanical problem.
Low fuel pressure could also do it.

wheel bearing or axle shaft

The PO 316 is still misfires om first 1000 revolutions
so the shop did a poor job for you on resolveing the
cylinder misfires

Try a diffferent shop

Have to clean the MAF Sensor & replace upstream
oxygen sensors if over 100,000 miles

Need the correct oem spark spark plugs/any brand

No reason the gas filter should be clogged unless it was in
the car for 10 years

Fuel pressure should be checked

Need to check for cylinder misfires on a road test of 20
miles or more with professional software in Mode#06

the fan will turn on when the engine temp reaches a set temperature and will only turn off when the engine drops below a certain temp and on the highway running hard it may stay on longer

You need to get the fault code scanned to be able to get an idea of where the problem is. It's possible you have a coil pack that goes bad when it heats up.

check engine light on?

Your radiator fans are not working .