Basic Circuit Breaker trips inconsistently, persistently
There are a few possibilities, if this is a standard breaker.  If it is AFCI or GFCI, there are a few other things to check, but you didn't mention that.


There is a high-current draw on the breaker that you are not aware of.  When the breaker trips, you can check the temperature of it with a non-contact thermometer.  If it is warmer than the breakers around it, that would indicate a high current load.  The internal heat is one thing that causes a breaker to trip.  You can also check the load with a clamp meter after removing the cover for the panel (you might not be comfortable with that).
The breaker is bad.  This happens, but its not very frequent.  Replacing it requires removing the cover of your electric panel (again,  you may or may not be comfortable with that).  It's a simple a cheap item to replace, so if there isn't a high load and its still tripping, this could be a good next step.
There is a bad connection to an outlet or light that shorts out periodically.  This can be the hardest to find, so that's why I suggested replacing the breaker to rule it out before hunting for this one.  The only way I know of finding this is to inspect every connection downstream from the breaker to find a loose or charred connection.  Any outlet that is loose in the wall or doesn't feel right when plugging something in would be suspect.