Yeah I managed to buy a few house improvements, but didn't have enough money to buy them all. After a few more days of playing I had enough gold and now there is no option to improve Breezehome :/. Anyone know what's going on/how to fix this?

I had the exact same problem with the Whiterun steward. Bought a house, didn't have enough gold for anything else. When I came back, the dialog option to buy furniture just wasn't there anymore. It reappeared a couple of play sessions (or in-game days?) later, no idea why...

That's all I've got...

Maybe you weren't there during regular shop hours of 8am-8pm?

It seems that you need to strike up a conversation during daytime, only when he stands near the jarl. Indeed that option isn't available otherwise, neither when he rests in his bedchamber nor spends time on the balcony.