It’s really great that you understand your dog and his working time periods.
You say Wolfy loses enthusiasm if he works more than 3-5 minutes. What happens when you periodically increase the searching period and reduce the rest period? Does the anticipation of the impending rest (reward) increase his working time? If you always train for 2-3 minutes has Wolfy become ‘stuck’ in that pattern of work. What would happen if you carried out a variable ratio on working times to rest times to extend Wolfy’s searching time whilst keeping his enthusiasm up.