Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
I understand the gravity of the situation. Equipment that does not work in such a situation is intolerable; you must be aggrieved by it by now.
What range extender was it, that was recommended? if a cut-rate brand, it might well be that it simply was defective out-of-the-box.
On the other hand... you might have a room that is subjected to strong radio
wave emissions (-I can't see the room in question, I don't know what local factors it has, I'm just guessing and considering every possibility...), and thus any signal might be 'jammed'. Do you have a laundry room nearby, or a furnace room/utility room, or similar industrial-equipment-installation site, that might be affecting the bedroom ?
If that isn't the case, then you're probably right, and the metal stairwell is blocking signals. (A way to judge, would be to use the phone while slowly rounding the corner into your bedroom. If the signal cuts off clean as a shadow on a sunny day, then the stairwell is the problem. If it fades off... that's more likely jamming.)
But I suspect that if two people did the effort and didn't get a good result, you may just have a defective range extender, and you should return it, in the original packaging, to the store or vendor you got it from, for an exchange for a working or closely equivalent device of equal value.
(You could try the extender, or the new extender, right in the same room with the base station of the phone system, first. That would give it a better chance, if signal interference or 'jamming', or signal reflection - which it occurs to me, can also be a problem - is the issue.)
Let me know what maker and model # ***** recommended range extender is, if you like... I might have more advice to offer, or a critique of that device.
(If this completes the question as far as you are concerned, please rate my Answer - favorably I hope - so that I may be paid for the time and care I have spent on your question. Thanks, ***** ***** luck.)