From my own experience, you need to nip this in the bud fast.
I used to create full 1 minute explainer videos + articles for $30 for a regular client who knew he was getting a good deal. Sadly, he started taking extreme liberties and I found myself steadily getting behind on more profitable orders. In the end, I therefore closed him down. I gave him fair warning that I could not keep offering reduced prices if he was going to be rude and never provide full order details. Then I just cut all ties when his behaviour became even more eratic.
More recently, I have had a client who has been ordering a standalone 1 - minute video package but requesting with each order that I also deliver 30-second edited down videos also. I reluctantly did this FOC since the client is regular, however, recently they started requesting 4 versions of the same video. I branded video, one non-branded video and a 30-second version of each also.
Very reluctantly, I did this. However, then the same client asked me to revise an order marked complete in October 2016 due to their brief changing. I Informed them that this would be $20 (a steal price considering I had to remake the entire video), only for the client to blow up at me saying that they thought they had 2 revisions with each order.
I was actually shocked by the cheek of this but didn’t back down. The client then paid and all was well until a few days later they placed an order and then (I think as revenge or them trying to make a point) messaged me asking me to cancel as they had decided to use another service provider.
This really bugged me. However, I have had the last laugh, as in agreeing to cancel, I disclosed that this would severely affect my Fiverr rankings and that as such, I would no longer be able to provide discounted work for them in future should they ever need me to.
A week later, they were back with their tail between their legs and there I was ready and waiting with a $50 quote which they have had to accept since no one else can provide them with the quality they need at anywhere near that price.
My Point? I let both the above situations drag out and get steadily worse the more they did. I will never let this happen again and if I was you, the next time your client orders, I would inform them that the price only covers 1 image and that this will be all you will be delivering. Take screenshots of any subsequent conversation and if the buyer leaves a nasty review, go to CS.