"I'll get feedback from my client and call you back straight away."
If candidates were paid a dollar every time a recruiter says this, they could well be filthy rich.
Unfortunately, candidates don't get paid and recruiters keep saying it anyway, although it could be the last time you hear from them.
This is a grave shame. Unless you are an accountant, I assume you take your career seriously. Therefore, you need to know exactly where your strengths and areas for improvement lie.
If you want recruiters to actually call you back when they say they will, you will have to take matters into your own hands. I recommend you try the following:
1) Have low expectations but withdraw your cooperation when they're not met
There are two levels of feedback.
One is feedback from the client explaining why they rejected your CV.
The other is feedback from the client explaining why they rejected you after interview.
The first is the hardest to extract, and the most important. If you are not progressing beyond the CV stage you really need to understand the reason.
One answer you should never accept is: "they chose somebody with more experience". This vague comment helps no one and is made by those who are too selfish to provide feedback for candidates who won't earn them a fee. If you find yourself in this position your best option is to refuse to work with that recruiter again in future. Ever.
2) Be initially patient
If you've attended an interview, congratulations.
Now prepare for a long wait. Your recruiter is dealing with an extremely pressurized and understaffed hiring manager. The absence of feedback is probably a problem within the bank's process and not with your recruiter's work ethic. The HR process in banks can be lengthy so expect delays.
3) Be latently pushy
If you've been waiting more than a week and you've heard nothing, be proactive.
If you pressurize your consultant, he/she will have to pressurise the client.
After all, if you are an outstanding candidate you are in control. The banks know there is a frightening scarcity of talent and if they don't move quick enough they'll lose out. If your consultant doesn't act upon your requests, politely remind them there are plenty of other agencies calling you.
4) Contact the client directly
If a fortnight has passed and you've heard either nothing or just a feeble excuse, call the client directly.
If you are serious about getting feedback, you may need to be this proactive but ONLY if all other attempts via your consultant have failed.
If none of this works. Give up. Stop applying for jobs, stay where you are. Or take up accounting.