I've been running into this issue a lot recently. I go the source panel in chrome dev tools in order to debug some javascript. In the past I've clicked onto a line where I want the debugger to stop. The line number turns blue, then when I trigger the function call, the program stops and I can look at variables.
Recently I've run into a situation a couple time where I try to click into a function, but the display indicated I'm not setting a breakpoint. The thing that's common between both time is that I'm working with Immediately Invoked Function Expressions(IIFE). Is it possible to set breakpoints in a iife without access to the source code?
You mentioned being able to set a breakpoint in an IIFE without access to the source code, so I setup two examples that you can try where you do not have access to source assuming you meant local disk. In either example, I was able to set a break point on any of the relevant IIFE lines and step into/over as expected using Chrome.
BTW - In neither example did I experience the behavior where Chrome did not set the breakpoint as expected.
JSFiddle: https://jsfiddle.net/iamwaltuo/fu1pcwqf/
Dropbox: https://www.dropbox.com/s/khlmi6c2fezv0tn/iifetest.html?raw=1
<html>
<head>
<script type="text/javascript">
(function () {
var i = 0;
console.log("i = " + i++);
console.log("i = " + i++);
})();
</script>
</head>
<body>
Check the console
</body>
</html>