The fuses only protect what's on the load side of the fuse. From the looks of the video, you only have the contactor, overload, and the motor that can possibly be the "Electrical" issue or possibly a loose wire on the load side of the fuses. Even a single lose wire can cause more than one fuse to fail, when the motor is "single phased", current (Amps) go up on the two phases left which can cause the remaining fuses to fail. But the Overload should trip if this were to happen...Unless set too high!? Surprised the control box has both fuses and overloads?
All 3 phase wiring between the fuses and breaker box should be protected by a 3 phase breaker. How many amps is the breaker? The control box shouldn't be fused more than the breaker rating, otherwise the fuses are useless....
For starters, I would turn power off to that bay at the "Breaker Box"...Check supply wires to the fuses to "MAKE SURE" you don't have any voltage before proceeding...If you don't have an ohm/voltage meter, get a good one. and learn how to use it or all your profits will end up in the electrician's pocket. Once you've made sure no power is at the line side of the fuses, Then tighten all the Line and Load wires attached to the fuses, contactor, and even check the overload connections, line and load. Then open the electric cover to the motor and tighten all the connections or check wire nutted connections...Now you've eliminated all possible connection issues.
If you don't feel comfortable doing this, call your electrician back and have him go through the steps above. If all is good, sounds like an intermittent motor issue, which is unlikely, or a possible bypass regulator failing that might be over pressurizing the pump and motor causing an overload. Adding 30a fuses will eventually let you know where the issue is, but the cost to fix will go up!!! Not good practice...
One last thing...Is this the only pump and control box wired like this? If you have more than one, use a clamp meter to check load amps between the different control boxes to see if they are the same.
Other than that, I am out of suggestions....