I feel the RNG is different after getting to room 46.

[Corinthas]

Before I got to the room I felt i was having a lot more luck with the draw and items found.
Now I have not seen the vault keys once for example since reaching room 46.. before I had found it a few times but never drafted the vault at the same time..

[adrien_perleflamme]

As you unlock more progress, you also generally add more rooms to your draft pool, beyond the 43 slots you have for interior rooms. So it's not abnormal for the vault room to be less common (it's more diluted in your draft pool, to continue the in game pool metaphor) and, as a result, to be drafted even less frequently at the same time as obtaining any specific item.

In my experience, the coat check is very important.

Also, I suspect picking up the compass increases your chance of drafting rooms facing north and, as a result, of even less commonly drafting dead ends (including the vault, obviously).

[yamitami]

you can also manipulate rarity in a few different ways, the wrench lets you adjust the rarity of gear rooms and the conservatory lets you adjust rarity of a random three rooms each time you enter. while the former doesn't affect the vault and the latter only has a chance of it, by making other rooms more rare you can get better odds for rolling the vault

the trading post can also get you the keys, especially when paired with the coat check. if you get the trading post then make your run about getting a lot of items, then head back out and trade away. i got one of the vault keys that way

if you happen to have the moon pendant then you can also use the trading post to guarantee the vault key (or any other given item) stays with you. trade the items you don't want to carry over until it gives you regular keys or dice until you only have the pendant and the vault key. that way it's a guarantee that the vault key (and pendant) will be with you on the next day