Cooktop burner doesn't stay on on low heat setting

Dear helpful repair people,
I have a 14-year-old GE Profile electric cooktop (smooth top). One of the burners cooks fine on med to high temperatures, but when I turn it down to the low heat (to keep a soup warm, for instance), the burner turns off completely. It also appears to not go on at all if I turn it one to a low temperature from the off position.
So, is this likely to be a burner problem or a switch problem? And, on a 14-year-old appliance, if I fix this, is there likely to be another problem soon? Fix or replace?
Thanks for any help!

Most likely the problem is a bad switch for this burner. The switches are different for different burners, so if you need the correct part number then post which burner is bad.

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… if I fix this, is there likely to be another problem soon?..

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It is unpredictable.

Here are the breakdown diagrams and Replacement parts for General Electric JP350WV1WW Electric range | AppliancePartsPros.com

Gene.

Thanks, Gene.
This is the front, left burner, 8 inches.
And I assume I’m looking for the infinite switch, not the "control element" - both of which are labelled as part 19 on the diagram.
Does it make any sense to replace the switch on the 6/9" burner, which I use almost as much as the 8 inch burner? (If one switch goes, is the next switch likely to go soon, too?)

Thanks again!

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…I assume I’m looking for the infinite switch, not the "control element" - both of which are labelled as part 19 on the diagram…

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All of the switches are infinite and I do not know why GE called some of them "control element". It sounds really strange to me.

The correct infinite switch [part]AP2631452[/part]

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…Does it make any sense to replace the switch on the 6/9" burner?..

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These switches are not cheap, so why you have to replace all of them if they still work?

Gene.