I think the other guys answered pretty well here but ill just toss in my 2 cents.

Being good looking helps tremendously for getting your foot in the door, but if you're awkward it kills their attraction quickly. some girls might tolerate it more than others and generally speaking the better you look the more you can get away with it, but she can totally find you physically attractive and then get the "ick" because your confidence wasn't congruent with your looks.

if a chick rejects you just next her and forget about it. you can't negotiate attraction. she might decide she wants you later but that's her prerogative at that point. dont waste your time waiting around or trying to ask her out again.

a girl smiling at you could be an IOI or she could be smiling because she thinks you're a dork and finds it amusing. IOIs can be tricky to decipher. it's likely her initial expression was an IOI but later changed to one of amusement rather than attraction after she rejected you.

I'm more or less re iterating what other guys said here but dont be an orbiter, dont catch oneitis and work on your game. looking good is great but having game is also important. girls are sensitive to discrepancies in your behavior and if you look like a Chad but dont act like one that incongruence is going to turn them off.

once you've turned a girl off and she has categorized you in her mind as not good mating material it is much more difficult to get a second shot with the same girl than it is to simply learn from your mistakes and do better with another one starting from a blank slate.

use this as a learning experience and GFTOW

Remember Charlie Brown, Lucy, and the football? Once you are rejected, be polite but otherwise cold and unengaging. Don't attempt to have conversations to gauge interest.

I‘m exceptionally goodlooking so maybe that changes the dynamic.

????This is a question use a question mark.

I am quite inhibited when it comes to approaching women

Fix that problem

So here's the problem with IOIs. They are absolute bullshit. Some girls are just friendly. Some may smile and that doesn't mean that they want to sleep with you. It's called being social.

Let me break this down into more simple terms. If a girl says yes to going out with you, that's an indicator of interest. If she initiates a flirty sexual conversation. That's an indicator of interest. If she becomes your girlfriend, that's an indicator of interest. You can sit in imaginary land and and misconstrue vague signals as interest. The truth is, you're just wasting your time and your energy on someone that could not give a shit.

Girls like attention. Actually guys do too to a lesser extent.

Provided you did not creep her out, get butt hurt or look pained and needy when she rejected you, she has no problem having you as an orbiter. Not an inner orbiter who might get to bang in the absence of Chad or a high value beta but you are welcome to an introductory level membership of her outer orbit where you can bask in her glory and add to it with your devotion.

Spin it round the other way. A nice girl that you don't want to get involved with just made advances to you but you said no -maybe because she is ugly, maybe autistic, maybe too needy. maybe she is dating your friend. Anyway provided it didn't go badly, you will feel a bit sorry for her, you will want her to know you didn't dislike her personally and you won't actually mind the idea that she wants your dick, so long as she isn't getting stalkery why would you not acknowledge her? Why would you not be friendly? If you were a bit selfish you might even just give her the odd breadcrumb of interest, just to keep seeing that look in her eye. Even though you don't want her, it still turns you on to feel wanted right? Now multiply that pleasure in being desired by 10 and you have a woman.

Right guy. Right Time. Right place.

If you don't happen to satisfy all three women will sort of keep you in orbit until or unless you satisfy all three.

At which case either up your game or next them. There is no pussy password — you guys need to just next them immediately if they don't play ball. At best keep them on the back burner till they try to fuck you.

But most of you guys can't mentally stomach the idea of putting a woman on the back burner and actually keeping her there without investing in it.

but just a few weeks later when I saw her again and she was giving me IOIs again, smiling at me.

She's playing with you. She's giggling with her friends and saying, "Watch this." then winks and smiles at you just to make a fool out of you.

I’m talking about girls I would see on a regular basis

Don't be an orbiter, my dude. If it's not a yes immediately, then it's a no automatically.

Why does this happen? What should I do about it?

You lack confidence and are putting pussy on a pedestal.
Women can smell a Beta from a mile away.
Remember this phrase whenever a woman opens her mouth: What's in it for me?

Is it fair to treat this as an invitation to talk to her again?

No. If she's interested, she will approach you.

I would try to have a low stakes conversation first, then gauge interest based on that.

Absolutely not. Playing it "safe" is the fastest way to rejection.
There's nothing more attractive to a girl than a man who knows what he wants, and does what it takes to get it.
Figure out what you want from a girl. Then go get it.
Remember, there are thousands of girls around you this very moment who are ready to step up to take her place.