It is quite weird, it does not affect me in any negatives way though. But it is still odd. I play on pc, got the game two days ago. Any ways to fix this? Or is this part of the game? (Which I doubt. )

Or do they lose gold, but I can't see it? This is confusing.

Merchants in Oblivion have unlimited gold. Meaning that the gold shown is only the highest price a merchant could possibly buy that item. I am unsure if a mod exists but it most likely will.

Oh, I see.
Thanks for telling me.

How much gold to buy a merchant has is not nescessarily how much he is carrying on his person.
Generally it is an item in his vendor chest making this gold available to buy things from the player.
See the creation kit for details on this.

The Riverwood Merchant has possibly the largest gold amount once you finish his retrieve the claw quest, and complete the barrow as well for other needed items later in game.
He just needs time to respawn/restock to show it.