I was told by an Apple support person that this is caused because the watch and iPhone are connecting at the same time. He had me disable the bluetooth connection with my watch and everything worked fine. My own experience supports this, at least sometimes! When I go to airplane mode on the watch, Siri works every time. However, today I went to Settings>Bluetooth on both Watch and iPhone and as soon as I opened the airpod case, both the watch and phone connected AND Siri worked! Furthermore, Apple's own website contradicted what the support guy said: Use your AirPods - Apple Support (look under "Listen with your Airpods") it explicitly says both are connected at the same time.
Regardless, Siri works fine when I am not connected with the watch and only works some of the time when I am connected to both. Apple needs to fix this! I shouldn't have to put the watch in airplane mode (effectively turning off Bluetooth) everytime I want to reliably use Siri on the Airpods