Hello and Welcome..
My name is ***** ***** The previous expert that was helping you has opted out of this question - so I can come in and help you from here..
I have read through all that you have been discussing..
I note you say the Engine fault light does not come on when you have this fault...
The Polo you have, while a modern vehicle with fuel injection , is a relatively simple design when it comes to engine management..
I note you say, when you get the problem of loss of acceleration, it doesn't die altogether, but it rattles... This rattling may well be caused by the hydraulic valve lifters in the engine.. it could be simply because the revs are so / too low.. or, it could be a part of the problem... You need to determine with this, if the engine is getting too hot.. If it is, you have a cooling system fault - and that will cause you all of this... In which case , that then needs further investigation.
If its proven not to be that - then - as you say, when you switch it off - and then on again and it then runs ok.. this is indicative of one of two faults... either you have a clogging fuel filter - or, a clogging / restriction inside the exhaust.
What happens is, either as above - while running, pressure causes it to eventually clog - then when you switch off - the pressure subsides... then you can start and run ok again... until the next time it happens.
So - first thing will be to have the fuel filter renewed.... and then see how it goes. If that then fixes it , thats great. IF not - then you need to have the exhaust system - inc the catalytic converter checked out for faults... Replacement is the only answer so you need a good garage to check / diagnose this properly.
I also have a final concern on the throttle body too.... Do ensure that this is all ok... cleaned fully etc... In some cases they have to be renewed if they give persistant problems....so ensure you properely rule faults out as mentioned above first.
Working through as above - you will get this sorted out.
Let me know how you go..and / or let me know if you need anything further on this..
~>>~~>>~ Meanwhile now at this point- Please do click on the "Exc / Ok rating" for me at this time.. "Thank you" in advance for that .
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Best Rgds, MIKE