Before anything else, ensure that you are properly securing the master link as this is the most common point of failure.
You should replace your cassette when you replace the chain. The chain and cassette wear fairly evenly. If one is worn out so is the other, and running a new chain on a worn cassette will wear the cassettechain faster.
If the gears are slipping then the cassette may be worn out and/or the derailer(s) are broken and/or in need of adjustment. The derailer hanger might also be an issue.
The SRAM pc-951 is an extremely common chain and in the dozens I've put on I haven't seen any snap on their own after such a short period. It's probably not quality of the chain, and something in your drivetrain is damaged or in dire need of adjustment.
There are a lot of points of failure in a drivetrain; go to a shop, a good one will take a quick look for free.