Before I could answer the original question, I would need a fuller understanding of the business purpose and development model behind the question. The only best universal answer is "execute a collaboration agreement before commencing work." The expectations of both parties must be set forth in writing so as to minimize misunderstandings and missed expectations.

Agreed. Although it does sound like the conversation has steered away from the original purpose of the thread. Which boils down to developers needing to realize artists may not share the same passion about your game as you do and therefore might not be interested in assisting in the continued development of the game and artists understanding that a simple 'no thanks' is all that's needed (in most cases. If I learned anything it's that there's always an exception and people love to point it out).

The entire comment above is extremely idealistic, especially when I mentioned that this post is specifically for minute budgets. What you want from artists is what many professionals provide; a detailed, vested interest with their own small bits of input. I have one very wonderful, long-term client who I provide hours and hours of free consultation time to as far as story, design, and the like, because while he's a great coder, he's clueless about the art and story sides of video games and I constantly make suggestions on what could make his game better.

But he has a market rate budget for what he asks. I know I am working for a fair wage and it makes me interested to see a project that he loves so much he is willing to invest that kind of money into, and gets me more excited to work on something he's really putting everything into.

Otherwise?

It's pretty damn ballsy to expect an artist to do more than you paid him to do "to make a better game", especially when non-artist game devs rarely have a real clue how much work can go into one piece. I still have people looking at me doing one picture for 15 hours and asking why I'm stiiiiiiiiiill on that same old picture. Most devs looking for artists just see the quality they want and don't pay attention to how much time the artist needed to do it, only that they can do it.

If you want people to be very talented and also very invested in your game, you have two choices. Get REALLY lucky, or pay them for their interest. When you don't pay, you will not get as much interest. Call them "unengaged" if you want, but "engaged" costs money in most cases. Why would you expect an artist to do anything but a quick, low detail job if you can only afford to pay them minimum wage or less? Again, apply it to your own life. If you charge $1000 to do a certain project to the best of your ability, a number you selected to account for the average time you spend making it the best you can, and someone begs you to lower than price to $100, do you think you will spend the same amount of time getting it to the best you can? Getting realistic is one of the biggest things indie devs fail at, and expecting artists to immediately find themselves enraptured in your idea to the point where they will double and triple their hours on a piece they aren't getting paid extra for isn't realistic or smart.

The statements quoted above are all facts of the business:
When you are broke and paying an artist below a certain amount, you should essentially expect they will cut the time on your project for other, higher paying projects. That doesn't mean that they will, but you should plan ahead with that expectation clear in your mind.
Asking for many edits without paying extra will anger your artist. It would anger anyone.
If you are broke and actually want to keep a decent artist with your project, you need to give them the benefit of the doubt and more. If that's "special" to you, then pay more. If you can't, you'll likely need to just plain deal with it.

In the end, it all comes down to the simple adage: Beggars can't be choosers. All game devs want their artists to be excellent, fast and cheap, and the fact is that you just can't realistically expect to get that diamond in the rough that is all three.