Obsession
When can I take special actions, and are there limits?
The rulebook's Special Actions section lists the costs and the designer confirmed the timing and the once-per-turn market limit.
Any time during your turn, even mid-favours and after reputation has gone past maximum (spend it first so nothing is wasted). Borrowing pounds (2 reputation per £100) and refreshing servants (3 each) can be repeated as often as reputation allows; refreshing the market costs 4 and is allowed once per turn as a special action (Useful Man and VP-card refreshes are extra).