First I realize this is somewhat an old thread but feel it was not answered well.
I found that Keychain closes quickly, possibly for security reasons and by, under Keychain Preferences, first aid, selecting "keep keychain open" when logging in it tends to not re ask me for keychain access.
Also somewhere there was a selection to allow keychain to stay open for a selected time period. I selected for it to remain open..
This quieted down the requests across all my computers.
Hope this helps .. someone.