Need some advice on applying for a job I really want. should i email them after being unsuccessful in a prior interview

I applied for a job in March and had an interview at the start of this month. The interview went really well and what was supposed to be a 45 minute interview was an hour and a half interview as the interviewers and I were getting along really well.

Anyway, I was unsuccessful for the role, which isn't exactly unsurprising as it is a role that I haven't had direct experience in but it's definitely where I want to work. Stupidly I didn't ask for feedback as the rejection email I received was really generic and I was a bit to disappointed to feel like chasing it up.

Anyway, not even four weeks later the same job has been advertised. I have put my application back in but I am wondering if I should email them and just make them aware of how keen I am for the role and that this is where I want to work and that I am willing to work hard to learn the ropes.

I don't want to seem pushy or give them a reason just to turf my resume out straight away, so any advice you can help me with is greatly appreciated.

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