It is likely that a currency could change in a post-apocalyptic world, just as it has happened in the past. Throughout human history, the currency that was used has been everything from paper money, coins and tokens, beaver pelts, wooden sticks, shells, etc.
In theory a currency can be anything that is agreed upon as a form of payment. The US Dollar is considered fiat money. There isn't anything to back it besides the belief that it has value. US Currency used to all be backed by Silver, and Gold, but those days are long gone. Gold and silver coins have also been taken out of circulation. Strict laws were even passed that prohibited private people from owning gold. There were stiff penalties for holding onto the gold, which sometimes meant prison sentences. The cases were rare, but served as a deterrent for most people.
In the Fallout series, bottle caps are the primary form of currency. They can be used to purchase goods, and services just like the Dollar does today. This is the current accepted form of currency, but it could change in favor for a different form. The reason why they are accepted is that there is a limited amount of them, and there are enough around to circulate.
To understand why a particular form of currency is accepted, you will need to start getting into economic theory. The basic theory involved is with supply and demand. There are enough bottle caps around that can keep the economy moving, but there are not so many, that they can be found in over abundance. If someone stumbled across a couple billion of them and started to spend them all, then there would be inflation since the value of each individual bottle cap would decrease. If this went on for a long time, this could cause the currency to collapse.
As the population increases, there could begin to be a shortage of bottle caps, and the economy would begin to grind to a halt. This would be the equivalent to a depression. This has happened several times in American history. This is one of the reasons we had to abandon the gold standard. There simply was not enough gold available to be circulated for it to work. It was becoming too expensive to produce coins because the cost of the metal exceeded the face value. This is also what happened to silver coins.
The shortage of bottle caps could be caused by any number of reasons. There is no real banking system in Fallout, but The Brotherhood does have control over the supply of bottle caps. They could keep accepting them as a form of payment, but when they buy things for themselves, they would use another type of currency and stockpile the bottle caps. Eventually, there wouldn't be enough bottle caps in circulation, and the bottle cap economy would crash. If this was to happen, then bottle caps would fall out of favor, and it would be replaced with something else.
What could also happen is that the supply of bottle caps could be inflated by The Brotherhood. They could find a way to infinitely produce new bottle caps to pay for their cause. When the value of them gets so small that you would need trucks full of them to purchase anything, then naturally another form of currency would replace it.
In summary, the bottle cap could lose its status as a currency if there is either a severe shortage of them, or they begin to appear in such abundance, that nobody is interested in using them.