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you don't say what model and engine size and fuel type the is but I'd say it sounds like a lack of fuel and could be a lack of fuel pressure from the electrical pump atthe tank.
If the connections to the pump are corroded or damaged then the pump could stop at any time or could not be running at full speed. Check that its relay switches in and outand the relay contacts are clean and bright – replace the relay if in any doubt and do the same for the fuse,
Ideally measure the pressure at the injectors and if this is low check the pump as described and also consider changing the fuel filter as if this partially blocked this too will reduce pressure.