Actually, it does sound exaactly like a breakpoint. The "Run without Pausing" option only appears if the VI was paused, which means it has. The most likely explanation is that you placed the breakpoint not on a wire, but on a structure (that while loop). If there are no breakpoints in your program, when you search for one, you should get an empty window saying no results were found. If there is one, it will take you straight to it, which might be interpreted as finding no results. Place a breakpoint in the code and search for breakpoints. See if you get two results. If you do, the other one is around the loop. It should appear as a red frame around the loop. To remove it, you need to click the breakpoint tool on the OUTER side of the loop border (watch where you click, because different places create different breakpoints).
If all this didn't help, post your code.
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