For some keywords, I see the Positions in Organic Keywords have not been updated for a long time. Can they be updated more often?

Our algorithm updates keyword data for Organic Keywords report depending on the keyword's estimated search volume, wherein the data for more popular keywords are updated more frequently. 

There is no option to initiate the update manually. 

We recommend using the Rank Tracker tool to see more frequent updates. In Rank Tracker, keywords will be updated weekly. You can also purchase Project Boost Max add-on for daily updates: