I'd agree with the idea that you pick your battles. Sometimes winning a battle at the expense of losing the war can apply to even simple things. You get the $15 and lose say 20 hours of your life to get it. I'd call that winning the battle but losing the war.
On the other hand, knowing how to successfully navigate a customer service issue can be a learning lesson best learned where the stakes are low. So pursuing the $15 not for the $15 but to learn how best to deal with ANY customer service problem can be worth your time.
Learn to document your time with Customer Service. That means, write down the time you called, the time you got through to a CS representative, the time spent and the outcome of that call. Write down any transfers to another person, write down the name of the people you talk to even if it is only a first name. Always ask for their name when you begin the conversation if they do not give it to you and try to get their full name.
Follow their 'formula responses' while being assertive but NOT aggressive or abusive. Tell the person if you are not satisfied with the response they give you and ask them to give you a supervisor to talk to. Document that exchange. This is important, often they do not transfer you to a supervisor, they either put you on hold and then 'drop the call' or simply hand you off to the representative sitting next to them. But it is important that you asked and document what happened. If you get that second person and again do not get the problem resolved, tell that person you are not satisfied with the response and ask to be transferred to their supervisor. Do this as many times as necessary and you MAY get it resolved. If not, then the fun begins.
By this time you should have been on the phone an hour or more. Now look up the phone number for the head office of the company and call. Ask for name of the person in charge of Customer Service for the company. Probably that is a Vice President. Ask to be put through to that person. Probably, you will get his/her secretary/assistant. Go ahead and explain to the secretary/assistant that you have spoken to their CS line, spent an hour (or more) on the phone, can document by the minute what happened and who you spoke to and have NOT gotten a satisfactory response. Say you now you want to talk to the person in charge since their system is not doing the job it should be doing. Your chances are around 90%+ that you will now get attention.
Years ago, I had a problem with a Jeep Cherokee. I called Customer Service and got the run around from one office to another for a couple of hours until everywhere was closed for the day. The next morning I tried again and got more of the run around. Then I called Chrysler's head office in Detroit and asked to speak to the VP in charge of Jeep. I got his secretary who told me he was in fact out of town. I explained my problem to her including a few examples of specific remarks that had been made to me and which I had written down with a time and name. Since her boss was out of town she asked me for my phone number and told me I would get a call from someone within 15 minutes.
After about 10 minutes my phone rang. The woman who was calling told me her name and that she was in the 'Executive Office' of Chrysler. She asked me if I had documented my calls as I had told the secretary. She then asked me to read all of what I had written down. Clearly, she was making notes and was not happy at what she was hearing.
Long story short, my problem got resolved immediately and at considerable expense to Chrysler. The owner of the dealership who ended up fixing the problem asked me, 'who do you know at Chrysler?' He told me he had never had a call from the Executive Office of Chrysler tellling him to solve a problem before. It was like having got a call from God. I later found out the 'Executive Office' consisted of 5 people including the then President Lee Iacocca. None of the other 4 members of the Executive Office had titles. They were just the 'Executive Office' and all had the power of God within Chrysler. I have no doubt she used the info I gave her to do some house cleaning within their system. None of that would have happened though if I had no documented everything or if I had lost my temper and became agressive.
Since then, I look forward to calls to a CS department. I'm polite, I'm assertive and IF I am in the right, I always get my problem resolved to my satisfaction. But you have to do it right, keep your cool and be persistent.
As for my experience with Chrysler, I sent flowers to the secretary of the Jeep VP, not the woman who actually made things happen. Why? Because the secretary was the person who 'opened the door' to getting things done. It's always nice to say thanks.