Security is one of our primary concern. To make Coinprism safer, we do not have access to the Bitcoins stored on Coinprism. We also do not store users' passwords, your private keys are encrypted with your Coinprism password before leaving your computer. We basically just provide a frontend to access Bitcoins and Colored Coins, this means we cannot view or spend your Bitcoins and Colored Coins.
This also means that Coinprism cannot access or recover Bitcoins and Colored Coins in the event that you lose or get your password stolen.
We then recommend downloading backups of your Coinprism wallet on your machine, you have the option to download your wallet encrypted (for which you need to remember your password to decrypt) or not encrypted (in case you're concerned with losing your password).