IR2110 high side switching problem
IR2110 driver works in high freqency switching mode. It cannot work (with the default schematic) in DC mode, like you want for your BLDC motor. This is because something should charge the bootstrap capacitor C1+C2. In HF switching the first low-side pulse pulls the output down, this reflects on pulling down the C1+C2 negaitve and they are charged through the bootstrap diode D1. If the high-side pulse occurs first it will be skipped until those capacitors are charged (until the next low-side pulse). In most applications this works fine.

For your application I see these options:
1) Get an isolated DC/DC with input 12V and output 12V and connect its output to the bootstrap capacitors. This converter does not need to be regulated, but is necessary to be isolated. Diode D1 is not needed.

2) Do not use this kind of drivers and go for a different schematic where high-side switches are P-channel. (depends on motor's voltage)

3) Get an IC capable of driving a BLDC motor. An example is L298 but you should check for your motor's current and voltage.