probable cause of damage to small SMD part: ESD, heat, something else?
It makes no sense to ask us.

READ THE DATASHEET.

The datasheet will tell you the maximum temperature the part can withstand and for how long.  For parts that are unusually sensitive to soldering, like some MEMS parts, there is also usually a recommended reflow temperature profile.  Follow it or insist that your contract manufacturer follow it.

Some parts are difficult to solder by hand due to the solder temperature and time restrictions.  You can do a few one-offs by hand and accept the failure rate.  Someone really skilled with soldering that understands the issues can make a difference.  But, for anything more than a few prototypes, you need to have these things soldered with temperature-controlled profiles.

Even your 10% failure rate is horrendous.  There really is no excuse for that.  From your description it's hard to say what exactly you are doing wrong, but the soldering temperature profile is my first suspicion.