Options:
Not enough air getting in.
EGR valve stuck.
Not enough fuel being injected.
Fuel not burning properly.
Injection timing incorrect.
Valve timing incorrect.
Low compressions due to engine wear or valves not sealing.
Air supply: Check the air intake system, from the entry hole, all the way to the manifold. Check for any obstructions or leaks. Ensure air filter is clean and not damp.
Is the throttle opening as required? Is it cable or drive-by-wire?
EGR valve: If it has one of these, check its operation. If it is stuck open, it will be allowing too much exhaust gas through when it needs air. Might need removing for a thorough clean.
Fuel injecting/not burning properly: Difficult to diagnose without specialist knowledge, training and tools. Some diagnosis may be possible from the exhaust smoke. When the engine struggles, what does the exhaust look like? More or less smoky than normal running, different colour? Normal is black, oil burning is blue, excess fuel can be white if the engine is running cold, or blueish, and smelly, if warm.
Injection timing/cam timing: Not known to slip, unless cambelt is slack or about to break, but worth checking the timing marks align, both for injection pump and camshaft.
Compressions: A compression test might be useful, but this requires diesel specific compression tester, expensive, so a diesel specialist would be needed.
How electronic is this engine fuel control? If it has a MAF (mass airflow sensor), ideally it will need connecting to a computer, with Fiat specific software, to see if the readings match the engine demand.
