I've got a friend like this, seriously flakey, but a very good laugh when she's on form.
I occasionally invite her to things when it's just her and me, but have learnt to invite her along with other friends, so I'm not left sitting on my own waiting for Godot.
The thing is though, that if it's a friendship, a real one, you'll be there for your friend.
Not just social events when she's a good laugh, but the other times also.
I pop over to my flakey friend and am amazed how chaotic her life is, think laundry everywhere, really dirty kitchen, sn kids, two crazy dogs, she works pt, her DH works away for months at a time, and I think her plate is just too full.
I hope I'm a good friend to her. I think friendship with flakey people is lovely, most have mental issues IMO, but you also have to meet them half way.
Sometimes official meet ups in restaurants are too much, and you might be better meeting up in a group, or in a more casual surrounding, like a park, or gallery or something like that where you are going anyway.
Flakes are wonderful company, but need tlc! You also have a role to play as her friend.