It won't let me buy any hoard packs in the crown shop. There's lots of room in the backpack so that's not the problem. Is there a limit how many you can buy?
What can also prevent you from purchasing packs are:
Treasure Card Space - If you've maxed out on treasures, you won't be able to purchase any packs as all packs contain chances of receiving treasures. So, ensure to sell any extras.
Reagents - Similarly to Treasures, if you've maxed out on a particular reagent (999), then the same fate will befall you. Transmute any extras into more of the rare reagents.
Crowns - I know this is most likely not an issue for you, but if one does not have enough crowns, the transaction cannot be completed.
There's no limit upon the amount of packs you can buy, just the amount of things you can store; items, reagents, treasures.