Is there a way to gain Sudden Insights down in the neath, and reliably so?
Chess with other players.
Chess with other players, a social action from inviting someone to do something intellectual in your lodgings, is your best and most consistent bet.
There’s also the Church-Great Game conflict card (a contact in the Great Game) which gives second chances if you side with the Church. This does have the advantage that its cap is higher than chess playing.
The Hedonist option on the Give a Gift card also gives one of every second chance.
If you’re in the middle of the University story line, there’s an available repeatably storylet that gives a Sudden Insight on success. Requires Tales of the University 9-23: http://fallenlondon.wikia.com/wiki/Talk_to_the_Porters
edited by PSGarak on 7/25/2016
If you still have the option to raise investigating in the university you can do the “Talk to the Porters” option to farm sudden insights.
You can reset your Mysterious Benefactor card for some Fate.
(I might have fancied doing this if I didn’t already have a Shadowy patron, because I’m not keen on the Society dips from loitering.)
Accepting gifts from Rubbery Men trades in your favours for a sudden insight.
If you’re still investigating the university, you can exchange 50 cryptic clues for a sudden insight, and then cash in the investigating for a few more cryptic clues in the Flit.
As a side note, most sources are capped at 20. If you want to gather more than that, you can receive gifts of second chances from another player; use the past benefactor card (if you chose the mendicant), or use the Candlit church dream card (req. chess dreams 8–10).