It's not difficult to imagine in-flight recharging from something like a KC-135 running a big fat generator. If you're recharging capacitors, connect time would probably be a minute or two.
What happens if the KC-135 misses the rendezvous? What if the charging port fails to work for some reason? What about the carbon footprint of these airborne generators?
Plus, now you have the weight of the capacitors to carry around all the time, further reducing the effective payload.
The same thing that happens today with combustion aircraft: the crew makes an emergency landing if they can, or bails out and waits for a Seahawk to pick them up.
This actually happens with fuel-driven aircraft regularly today.