Can I stop the game from asking me to reassign spies?

No this is not possible you have to reassign them every time.

I found that clicking the espionage overview is helpful to avoid making mistakes as it shows where you already have spies assigned - especially if you need to assign two to the same city for protecting different districts.

Updated answer: in newer versions of the game (tested without addons), there is now a button to repeat the previous assignment which makes the process fairly quick and painless compared to before.