Hello Gwenola,
I would look at your aquifer parameters:
In the aqu.aqu file, look at dep_bot (height of the aquifer) and set flo_min to this value, so you can have an aquifer response (in math terms dep_bot = flo_min).
Then you need to set a realistic sp_yld value, I don't know your zone, but let's suppose that you don't have a shallow aquifer, so a sp_yld between 0.1-0.15 should sustain enough aquifer flow.
After, try to set a realistic percolation for your zone. Once you feel like you're percolating well, try different alpha values (you can run the baseflow program which is in the SWAT website)
Good luck