This isn't the case if you loot everything (including theft in my case) and resell anything that isn't either named or used for crafting.
Right now I'm on Act II (Day 77). I've got 20.000c in my inventory, having bought 6-7 rare items from shops, and I've completely upgraded the Stronghold.
Also I don't think money is technically finite in this game since you get paid taxes every 5 turns (between 500-1500c at my Prestige level).
EDIT: Ninja'd. KingsGambit's reply is better anyway