Exactly, always matter price of bitcoin. Because bitcoin is bitcoin because of its price, if bitcoin go down and down, so it will be lose its repute and also its demand. Now people like it and want to invest in it, because bitcoin is going up and now it has a good time to give us money.
If now bitcoin suddenly down and an other crypto currency will come than people take turn and invest into an other crypto currency.
Bitcoin wont lose any reputation - first of all
There are still a few ways in which Bitcoin could lose its reputation, at least, to a degree. First, if its gets hacked big time. I mean someone finds a way to attack the cryptographic algorithm behind Bitcoin, which would allow to quickly find private keys to any Bitcoin address. That would undoubtedly turn out to be a complete fiasco and end of Bitcoin, though this is unlikely to happen. Second, if someone is lucky to generate a key pair already generated and used for storing bitcoins. That is also unlikely. And third, if Bitcoin Core developers continue infighting and a few long awaited updates get rejected in the end...
The latter seems to be the most likely event which would most certainly hurt Bitcoin