While loop using bluebird promises

cast can be translated to resolve. defer should indeed not be used.

You'd create your loop only by chaining and nesting then invocations onto an initial Promise.resolve(undefined).

function promiseWhile(predicate, action, value) {
    return Promise.resolve(value).then(predicate).then(function(condition) {
        if (condition)
            return promiseWhile(predicate, action, action());
    });
}

Here, both predicate and action may return promises. For similar implementations also have a look at Correct way to write loops for promise. Closer to your original function would be

function promiseWhile(predicate, action) {
    function loop() {
        if (!predicate()) return;
        return Promise.resolve(action()).then(loop);
    }
    return Promise.resolve().then(loop);
}

I prefer this implementation as its easier to simulate break and continue with it:

var Continue = {}; // empty object serves as unique value
var again = _ => Continue;

var repeat = fn => Promise.try(fn, again)
  .then(val => val === Continue && repeat(fn) || val);

Example 1: stops when either the source or the destination indicate an error

repeat(again => 
    source.read()
    .then(data => destination.write(data))
    .then(again)

Example 2: stop randomly if the coin flip given 90% probability results with a 0

var blah = repeat(again =>
    Promise.delay(1000)
    .then(_ => console.log("Hello"))
    .then(_ => flipCoin(0.9) && again() || "blah"));

Example 3: Loop with condition that returns the sum:

repeat(again => {
  if (sum < 100) 
    return fetchValue()
      .then(val => sum += val)
      .then(again));
  else return sum;
})