What to do if a pilot cannot understand an ATC instruction, after asking to repeat it many times? ?

Essentially nothing   You absolutely do not move until you know exactly where she wants you to be.  Even if you spend the afternoon on the radio repeating and questioning what she is saying you say put.  That keeps you out of danger since she knows where you are and it gives her the incentive to stop and rephrase the instructions more clearly.  In the event anyone ever questions your actions you'll have either tapes of the conversation from the controller or testimony from all the other pilots who will have been listening in with interest to the lingering conversation.  

You don't "guess" at what the controller says.  You tell them they make no sense, and ask them to "say again". 

If it was me, I'd make a report to the FAA.  They will play back the recording, and determine which of you has the problem. 

I filed a "near miss" report with the FAA when I took my "check ride" to get my license 40 years ago.  ATC caused a safety problem for me TWICE during my aporoach to land, with the FAA examiner in my aircraft!  He was pi$$ed at the controller!! 

Another time I contacted approach control (when I was not required) and asked for vectors and separation because I was inbound in minimum conditions, through the area of a well-used commercial airport, for the safety of myself and all traffic related to that airport.  ATC proceeded to give me a DF steer, making me fly in large rectangles, as if I was practicing.  I complained and again asked for vectors and separation into my destination airport.  ATC then filed a report to the FAA that I was "lost".  I was contacted by the FAA and explained, so they got the voice recordings and verified my story and made some action against the ATC "specialist". 

One other time I flew into Canada and the destination airport chewed me out for calling in late to the tower.  They showed me a Canadian chart that was very different than the up-to-date USA chart that I was using.  I talked to the FAA and met the guy at a training session that he was giving for pilots.  I gave him both charts and he got the erroneous USA chart updated and said I did a great service by reporting the ambiguity! 

So you need to contact the FAA because accidents might happen from these problems.  The problems need to be fixed.  You tell them the date, time, location and frequency.  ATC needs to use "clear" language and you need to understand it.

If you are still on a runway GET OFF IT.   If you are on a taxi way and do not know what to do.  STOP.  

A British Airways heavy (passenger jet) was approaching Hamburg and getting instructions, including runway turnoff intersection to the taxiway.  The pilot asked for confirmation and directions to get to the assigned gate.

"Speedbird 192, you have not been to Hamburg before?"

"Hamburg--Speedbird 192.  I have been twice before, but I did not land."

"Understood, Speedbird 192.  Here are your instructions again."

Spend more time doing nothing but listeniing to ATC and becoming more familiar with the instructions they issue. Your lack of knowledge and inability to understand is the problem, it's not the controller's fault. If nothing else, you could have called them on the phone later and asked for clarification.  

Explain back what you think she wants you to do in words that YOU understand and ask her if this is what she wants.

And since you were unable to derive a method to resolve that situation on you own, perhaps it would be better that you don't fly until you do.