I’m not great with UBAQs except for via BPMs, but are you logged in as a user who can usually update the unit price field in question manually?
Sorry if it’s a dumb question!
@vfeldt Along the lines of what @SteveFossey is suggestion we need to turn on tracing and then do the change in price lists to see what is called and what values are changed along with unitprice in the UI since we will need to mimic that in the UBAQ.
Do you have all of the keys to PLPartBrk in the BAQ? I would also include SysRowID in case we need to roll our own update.
Not a dumb questions, but yes! 
I will do the trace. Thanks for your help.