I thought it said that they only stocked 1 each rare item, 3 each uncommon and 5 each common.

Kiriska is right, each item's stock is unlimited!
Rare items stock for one minute, uncommon for three minutes, and common for the whole time! So you don't need to worry about grabbing items faster than everyone else and instead just have to time it right, which I really love. ^^

That is so reassuring! <3 I'm very glad to hear it.

Thank you very much for telling me, both of you.

Came here to suggest this exact same thing. Moreover, I don't think deflation would be an issue due to item prices not being too cheap.

I think this would be a good idea. I understand the one minute thing, but I feel like it is way too long.